A sphere and a cube have the same surface area. What is the ratio of the square of volume of the sphere to the square of volume of the cube ? -Maths 9th

A sphere and a cube have the same surface area. What is the ratio of the square of volume of the sphere to the square of volume of the cube ? -Maths 9th
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If a sphere is inscribed in a cube, then find the ratio of the volume of the cube to the volume of the sphere. -Maths 9th

Description : If a sphere is inscribed in a cube, then find the ratio of the volume of the cube to the volume of the sphere. -Maths 9th

Last Answer : The ratio of the volume of the cube to the volume of the sphere are as

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Sphericity is the ratio of the surface area of a spherical particle having the same volume as the particle to the surface area of the particle. Which of the following has the maximum value of sphericity? (A) Sphere(B) Cube(C) Cylinder (L/D = 1)(D) Raschig rings

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Find the radius of a sphere whose surface area is 154 cm square. -Maths 9th

Description : Find the radius of a sphere whose surface area is 154 cm square. -Maths 9th

Last Answer : Let 'r' be the radius of sphere Surface area of sphere = 4 πr2 ⇒ 154 = 4 πr2 ⇒ 154 = 4 x 22/7 x r2 ⇒ r 2 = 154 x 7/4 x 22 = 49/4 ⇒ r = 7/2 cm = 3.5 cm

A square has its side equal to the radius of the sphere. The square revolves round a side to generate a surface of total area S. -Maths 9th

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If the volume of a sphere is numerically equal to its surface area, then find the diameter of the sphere. -Maths 9th

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Last Answer : Let r be the radius of the sphere. and Volume of a sphere = surface area of the sphere ⇒ 4 / 3πr3 = 4πr2 ⇒ r = 3 cm ∴ Diameter of the sphere = 2r = 2 × 3 = 6 cm

If the volume of a sphere is numerically equal to its surface area, then find the diameter of the sphere. -Maths 9th

Description : If the volume of a sphere is numerically equal to its surface area, then find the diameter of the sphere. -Maths 9th

Last Answer : Let r be the radius of the sphere. and Volume of a sphere = surface area of the sphere ⇒ 4 / 3πr3 = 4πr2 ⇒ r = 3 cm ∴ Diameter of the sphere = 2r = 2 × 3 = 6 cm

Find the volume of a sphere whose surface area is 154 cm sq. -Maths 9th

Description : Find the volume of a sphere whose surface area is 154 cm sq. -Maths 9th

Last Answer : Let r cm be the radius of sphere. Surface area of the sphere = 4 πr2 ⇒ 154 = 4 πr2 ⇒ 4 x 22/7 x r2 = 154 r 2 = 154 x 7/4 x 22 = 72/22 ⇒ r = 7/2 Volume of sphere = 4/3 πr3 = 4/3 x 22/7 x 7/2 x 7/2 x 7/2 cm3 = 539/3 cm3 = 179.2/3 cm3

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Description : A cube and a sphere are of the same height. -Maths 9th

Last Answer : Volume of cube/ volume of the sphere = a3 / 4/3.π.(a/2)3 = 6/π (Let edge of cube be a then radius of sphere = a/2) ∴ Required ratio = 6 : π

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Last Answer : (c) Surface area of a cube = 96 cm2 Surface area of a cube = 6 (Side)2 = 96 ⇒ (Side)2 = 16 ⇒ (Side) = 4 cm [taking positive square root because side is always a positive quantity] Volume of cube = (Side)3 = (4)3 = 64 cm3 Hence, the volume of the cube is 64 cm3.

The lateral surface area of a cube is 256 m2. The volume of the cube is -Maths 9th

Description : The lateral surface area of a cube is 256 m2. The volume of the cube is -Maths 9th

Last Answer : (a) Given, lateral surface area of a cube = 256 m2 We know that, lateral surface area of a cube = 4 x (Side)2 ⇒ 256 = 4 x (Side)2 ⇒ (Side)2 = 256/4 = 64 ⇒ Side = √64 = 8 m [taking positive square root ... of a cube = (Side)3 = (8)3 = 8 x 8 x 8 = 512 m3 Hence, the volume of the cube is 512 m3.

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Description : If S is the total surface area of a cube and V is its volume, then which of the following is correct ? -Maths 9th

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Description : Find the ratio of the total surface area and lateral surface area of a cube. -Maths 9th

Last Answer : Let a be the edge of the cube, then Total surface area = 6a2² and lateral surface area = 4a² Now ratio between total surface area and lateral surface area = 6a² : 4a² = 3 : 2

A cube of side 5 cm contain a sphere -Maths 9th

Description : A cube of side 5 cm contain a sphere -Maths 9th

Last Answer : Each side of the cube (a) = 5 cm Diameter of the sphere (2r) = 5 cm . ∴ Radius of the sphere (r) = 5/2 cm Volume of the cube = a3 = 53 cm3 = 125 cm3 Volume of the sphere = 4/3 πr3 = 4/3 x ... /2 x 5/2 = 65.476 cm3 Volume of gap between cube and sphere = 125.000 cm3 - 65.476 cm3 = 59.524 cm3

The outer curved surface areas of the hemisphere and sphere are in ratio 2:9. find their ratio of their raddii -Maths 9th

Description : The outer curved surface areas of the hemisphere and sphere are in ratio 2:9. find their ratio of their raddii -Maths 9th

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The outer curved surface areas of the hemisphere and sphere are in ratio 2:9. find their ratio of their raddii -Maths 9th

Description : The outer curved surface areas of the hemisphere and sphere are in ratio 2:9. find their ratio of their raddii -Maths 9th

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Description : A sphere and a cone have equal bases. If their heights are also equal, the ratio of their curved surface will be : -Maths 9th

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A right circular cylinder just encloses a sphere of radius r (see fig. 13.22). Find (i) surface area of the sphere, (ii) curved surface area of the cylinder -Maths 9th

Description : A right circular cylinder just encloses a sphere of radius r (see fig. 13.22). Find (i) surface area of the sphere, (ii) curved surface area of the cylinder -Maths 9th

Last Answer : Surface area of sphere = 4πr2, where r is the radius of sphere (ii) Height of cylinder, h = r+r =2r Radius of cylinder = r CSA of cylinder formula = 2πrh = 2πr(2r) (using value of h) = 4πr2 (iii) Ratio ... sphere)/CSA of Cylinder) = 4r2/4r2 = 1/1 Ratio of the areas obtained in (i) and (ii) is 1:1.

Find the surface area of a sphere of radius: (i) 10.5cm (ii) 5.6cm (iii) 14cm -Maths 9th

Description : Find the surface area of a sphere of radius: (i) 10.5cm (ii) 5.6cm (iii) 14cm -Maths 9th

Last Answer : Formula: Surface area of sphere (SA) = 4πr2 (i) Radius of sphere, r = 10.5 cm SA = 4 (22/7) 10.52 = 1386 Surface area of sphere is 1386 cm2 (ii) Radius of sphere, r = 5.6cm Using formula, SA = 4 (22 ... 75 cm Surface area of sphere = 4πr2 = 4 (22/7) 1.752 = 38.5 Surface area of a sphere is 38.5 cm2

The surface area of a sphere of radius 5 cm -Maths 9th

Description : The surface area of a sphere of radius 5 cm -Maths 9th

Last Answer : Radius of the sphere (r1) = 5 cm Radius of the base of cone (r2) = 4 cm Let r сm be the height of the cone. Surface area of sphere = 4 πr2 ⇒ 4 π(5)2 = 100 π cm2 Curved surface area of cone = πrl = 4 πl ... ∴ Volume of cone = 1/3 πr2h = 1/3 x 22/7 x 42 x 3 = 352/7 cm3 = 50.29 cm3 (Approximately)

For a non-spherical particle, the sphericity (A) Is defined as the ratio of surface area of a sphere having the same volume as the particle to the actual surface area of the particle (B) Has the dimension of length (C) Is always less than 1 (D) Is the ratio of volume of a sphere having the same surface area as the particle to the actual volume of the particle

Description : For a non-spherical particle, the sphericity (A) Is defined as the ratio of surface area of a sphere having the same volume as the particle to the actual surface area of the particle (B) Has ... of volume of a sphere having the same surface area as the particle to the actual volume of the particle

Last Answer : (A) Is defined as the ratio of surface area of a sphere having the same volume as the particle to the actual surface area of the particle

A sphere, a cylinder and a cone respectively are of the same radius and same height. Find the ratio of their curved surfaces. -Maths 9th

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A 4 cm cube is cut into 1 cm cubes. Calculate the total surface area of all the small cubes. -Maths 9th

Description : A 4 cm cube is cut into 1 cm cubes. Calculate the total surface area of all the small cubes. -Maths 9th

Last Answer : Side of cube = 4 cm But cutting into 1 cm cubes, we get = 4 x 4 x 4 = 64 Now surface area of one cube = 6 x (1)² = 6 x 1=6 cm² and surface area of 64 cubes = 6 x 64 cm² = 384 cm²

Find the lateral surface area and total surface area of a cube of edge 10 cm. -Maths 9th

Description : Find the lateral surface area and total surface area of a cube of edge 10 cm. -Maths 9th

Last Answer : Edge of cube (a) = 10 cm (i) ∴ Lateral surface area = 4a² = 4 x (10)² = 4 x 100 cm²= 400 cm² (ii) Total surface area = 6a² = 6 x(10)² cm² = 6 x 100 = 600 cm²

an edge of cube is increased by 10%. find the percentage by which the surface area of cube has increased -Maths 9th

Description : an edge of cube is increased by 10%. find the percentage by which the surface area of cube has increased -Maths 9th

Last Answer : each side of cube=l incresed by 10%=L+L/10 =11L/10 surface area of the new cube= 6l^2 =6x 11L/10 x 11L/10 =726/100L^2 % increase= 726/100L^2 - 6L^2 / 6L^2 x 100 =126L^2/100 / 6L^2 x 100 =126L^2/600L^2 x 100 =126L^2/ 6L^2 =126/6 =21 %

The perimeter of one face of a cube is 20 cm. Find the lateral surface area of the cube. -Maths 9th

Description : The perimeter of one face of a cube is 20 cm. Find the lateral surface area of the cube. -Maths 9th

Last Answer : Let a be the edge of cube, ∴ Perimeter of one face of cube = 20 cm ⇒ 4a = 20 ⇒ a = 5 ∴ Lateral surface area of cube = 4a2 = 4 (5)2 = 100 cm2

The total surface area of a cube is 726 cm2. Find the length of its edge . -Maths 9th

Description : The total surface area of a cube is 726 cm2. Find the length of its edge . -Maths 9th

Last Answer : Total surface area of a cube = 726 cm2 6 × (side)2 = 726 (side)2 = 121 side = 11 cm Hence, the length of the edge of cube is 11 cm.

an edge of cube is increased by 10%. find the percentage by which the surface area of cube has increased -Maths 9th

Description : an edge of cube is increased by 10%. find the percentage by which the surface area of cube has increased -Maths 9th

Last Answer : each side of cube=l incresed by 10%=L+L/10 =11L/10 surface area of the new cube= 6l^2 =6x 11L/10 x 11L/10 =726/100L^2 % increase= 726/100L^2 - 6L^2 / 6L^2 x 100 =126L^2/100 / 6L^2 x 100 =126L^2/600L^2 x 100 =126L^2/ 6L^2 =126/6 =21 %

The perimeter of one face of a cube is 20 cm. Find the lateral surface area of the cube. -Maths 9th

Description : The perimeter of one face of a cube is 20 cm. Find the lateral surface area of the cube. -Maths 9th

Last Answer : Let a be the edge of cube, ∴ Perimeter of one face of cube = 20 cm ⇒ 4a = 20 ⇒ a = 5 ∴ Lateral surface area of cube = 4a2 = 4 (5)2 = 100 cm2

The total surface area of a cube is 726 cm2. Find the length of its edge . -Maths 9th

Description : The total surface area of a cube is 726 cm2. Find the length of its edge . -Maths 9th

Last Answer : Total surface area of a cube = 726 cm2 6 × (side)2 = 726 (side)2 = 121 side = 11 cm Hence, the length of the edge of cube is 11 cm.

The total surface area of a cube is 150sq.cm. Find the perimeter of any one of its face ? -Maths 9th

Description : The total surface area of a cube is 150sq.cm. Find the perimeter of any one of its face ? -Maths 9th

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The total surface area of a cube is 150sq.cm. Find the perimeter of any one of its face ? -Maths 9th

Description : The total surface area of a cube is 150sq.cm. Find the perimeter of any one of its face ? -Maths 9th

Last Answer : Take the side be s, 6s^(2)=150cm^(2) s^(2)= 150/6 =25 s^(2)=square root of 25 s=5 Area of square s^(2) 5×5=25sq.cm. Perimeter = 4×side =4×5=20cm

The lateral surface area of a cube is 576 cm sq. -Maths 9th

Description : The lateral surface area of a cube is 576 cm sq. -Maths 9th

Last Answer : Let each side of the cube be a cm. Then, the lateral surface area of the cube = 4a2 ∴ 4a2 = 576 ⇒ a2 = 576/4 cm2 = 144 cm2 ⇒ a = 12 cm Volume of the cube = a3 = (12 cm)3 = 1728 cm3 Total surface area of the cube = 6a2 = 6 x 122 = 864 cm2

How many small cubes each of 96 cm^2 surface area can be formed from the material obtained by melting a larger cube of 384 cm^2 surface area ? -Maths 9th

Description : How many small cubes each of 96 cm^2 surface area can be formed from the material obtained by melting a larger cube of 384 cm^2 surface area ? -Maths 9th

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The length, breadth and height of a rectangular parallelopiped are in the ratios 6 : 3 : 1. If the surface area of a cube is equal -Maths 9th

Description : The length, breadth and height of a rectangular parallelopiped are in the ratios 6 : 3 : 1. If the surface area of a cube is equal -Maths 9th

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The whole surface area of a rectangular block is 1300 cm2. Find its volume, if their dimensions are in the ratio of 4 : 3 : 2. -Maths 9th

Description : The whole surface area of a rectangular block is 1300 cm2. Find its volume, if their dimensions are in the ratio of 4 : 3 : 2. -Maths 9th

Last Answer : Let the length, breadth and height of the rectangular box be 4x, 3x and 2x, respectively. ∵ Total surface area = 1300 cm2 2(4x × 3x + 3x × 2x + 4x × 2x) = 1300 52x2 =1300x2 = 25x = 5 ∴ Volume of rectangular box = 4x × 3x × 2x = 24(5)2 = 3000 cm3

If the ratio of curved surface area and total surface area of a cylinder is 1 : 3, then find the volume of cylinder when the height is 2 cm. -Maths 9th

Description : If the ratio of curved surface area and total surface area of a cylinder is 1 : 3, then find the volume of cylinder when the height is 2 cm. -Maths 9th

Last Answer : Let the radius and height of the cylinder be r and h, respectively . Given that, Curved surface area / Total surface area = 1/3 ⇒ 2πrh / 2πr(h + r) = 1/3 ⇒ 3h = h + r ⇒ r = 2h = 4cm ∴ volume of cylinder πr2h = π × (4)2 × 2 = 32π cm3

The whole surface area of a rectangular block is 1300 cm2. Find its volume, if their dimensions are in the ratio of 4 : 3 : 2. -Maths 9th

Description : The whole surface area of a rectangular block is 1300 cm2. Find its volume, if their dimensions are in the ratio of 4 : 3 : 2. -Maths 9th

Last Answer : Let the length, breadth and height of the rectangular box be 4x, 3x and 2x, respectively. ∵ Total surface area = 1300 cm2 2(4x × 3x + 3x × 2x + 4x × 2x) = 1300 52x2 =1300x2 = 25x = 5 ∴ Volume of rectangular box = 4x × 3x × 2x = 24(5)2 = 3000 cm3

If the ratio of curved surface area and total surface area of a cylinder is 1 : 3, then find the volume of cylinder when the height is 2 cm. -Maths 9th

Description : If the ratio of curved surface area and total surface area of a cylinder is 1 : 3, then find the volume of cylinder when the height is 2 cm. -Maths 9th

Last Answer : Let the radius and height of the cylinder be r and h, respectively . Given that, Curved surface area / Total surface area = 1/3 ⇒ 2πrh / 2πr(h + r) = 1/3 ⇒ 3h = h + r ⇒ r = 2h = 4cm ∴ volume of cylinder πr2h = π × (4)2 × 2 = 32π cm3

The outer and the inner radii of a hollow sphere are 12 cm and 10 cm. Find its volume. -Maths 9th

Description : The outer and the inner radii of a hollow sphere are 12 cm and 10 cm. Find its volume. -Maths 9th

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The outer and the inner radii of a hollow sphere are 12 cm and 10 cm. Find its volume. -Maths 9th

Description : The outer and the inner radii of a hollow sphere are 12 cm and 10 cm. Find its volume. -Maths 9th

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If the radius of a sphere is 2r, then its volume will be -Maths 9th

Description : If the radius of a sphere is 2r, then its volume will be -Maths 9th

Last Answer : As, r=2r Volume of sphere = 4​/3π(2r)^3 =32/3​πr^3

If the radius of a sphere is 2r, then its volume will be -Maths 9th

Description : If the radius of a sphere is 2r, then its volume will be -Maths 9th

Last Answer : (d) Given, radius of a sphere = 2r Volume of a sphere =4/3 π(Radius)3 = 4/3 π(2r)3 = 4/3 π 8r3 = (32 πr3)/3 cu units Hence the volume of a sphere is (32 πr3)/3 cu units.

The radius of sphere is 2r, then find its volume. -Maths 9th

Description : The radius of sphere is 2r, then find its volume. -Maths 9th

Last Answer : Volume of the sphere = 4/3.π.(2r)3 = 32/3πr3

From a wooden cylindrical block, whose diameter is equal to its height, a sphere of maximum possible volume is carved out. -Maths 9th

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