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
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
Description : The lateral surface area of a cube is 256 m2. The volume of the cube is -Maths 9th
Last Answer : NEED ANSWER
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.
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
Description : Find the lateral surface area and total surface area of a cuboid of length 80 cm, breadth 40 cm and height 20 cm. -Maths 9th
Last Answer : Length of cuboid (l) = 80 cm Breadth (b) = 40 cm Height (h) = 20 cm (i) ∴ Lateral surface area = 2h(l + b) = 2 x 20(80 + 40) cm² = 40 x 120 = 4800 cm² (ii) Total surface area = 2(lb ... x 40 + 40 x 20 + 20 x 80) cm² = 2(3200 + 800 + 1600) cm² = 5600 x 2 = 11200 cm²
Description : 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
Last Answer : answer:
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
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.
Description : The total surface area of a cube is 96 cm2 . The volume of the cube is -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 : (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.
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
Description : The volume of a cube is numerically equal to sum of its edges. What is the total surface area in square units ? -Maths 9th
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
Description : Find the ratio of the lateral surface -Maths 9th
Last Answer : Lateral surface area of cube : Total surface area of cube = 4a2 : 6a2 = 2 : 3.
Description : Find (i) the lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2 m in diameter and 4.5m high. -Maths 9th
Last Answer : Height of cylindrical tank, h = 4.5m Radius of the circular end , r = (4.2/2)m = 2.1m (i) the lateral or curved surface area of cylindrical tank is 2πrh = 2 (22/7) 2.1 4.5 m2 = (44 0.3 ... ) = 87.12 m2 This implies, S = 95.04 m2 Therefore, 95.04m2 steel was used in actual while making such a tank.
Description : A right circular cylinder and a right circular cone have equal bases and equal volumes. But the lateral surface area of the right circular cone is -Maths 9th
Description : What is the volume of a right prism standing on a triangular base of sides 5 cm, 5 cm and 8 cm whose lateral surface area is 828 cm^2 ? -Maths 9th
Last Answer : Lateral surface area of a prism = Perimeter of base Height ⇒ 840 = (5 + 5 + 8) Height ⇒ Height = 8401884018 = 46 cm. = Semi perimeter of the triangular base = 182182 = 9 cm ∴ Area of triangle = 9(9- ... 4 1 = 12 cm2 ∴ Required volume of prism = Area of base Height = (12 46) cm3 = 552cm3
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 %
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
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
Description : Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the sum of the surface areas of the three cubes. -Maths 9th
Last Answer : Let each side of a cube = a cm Then surface area = 6a² cm² and surface area of 3 such cubes = 3 x 6a² = 18a² cm² By placing three cubes side by side we get a cuboid whose ... + 3a²] = 14 a² ∴ Ratio between their surface areas = 14a² : 18a² = 7 : 9
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
Description : If the lateral surface of a cylinder is 94.2 -Maths 9th
Last Answer : Height of the cylinder (h) = 5 cm Let r сm be the radius of the base Lateral surface area of cylinder = 94.2 cm2 ⇒ 2 πrh = 94.2 cm2 2 x 3.14 x r x 5 = 94.2 ⇒ r = 94.2/2 x 3.14 x 5 = 94.2 ... Thus, radius of the base of cylinder = 3 cm. (ii) Volume of cylinder = πr2h = 3.14 x 32 x 5 = 141.3 cm3
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
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
Description : Find the ratio of surface area and volume of the sphere of unit radius. -Maths 9th
Last Answer : Required ratio = 4πr2 / 4/3.πr3 = 3 x 4 x π x (1)2 / 4 x π x (1)3 = 3/1 (Since, r = 1) i.e., 3 : 1
Description : the curved surface area of a cylinder is 154 cm. the total surface area of the cylinder is three times its curved surface area. find the volume of the cylinder. -Maths 9th
Last Answer : T.S.A = 3*154 = 462 cm² C.S.A = 154 cm² C.S.A = 2πrh T.S.A = 2πr(r+h) Now, In T.S.A = 2πrr + 2πrh 462 = 2πrr + 2πrh 462 = 2*22/7*r*r + 154 462 - 154 = 2*22/7*r*r 308*7/2*22 = r*r 49 = r*r R = 7 cm ... 7*h 154/44 = h 7/2 =h H = 3.5 cm or 7/2 cm Now volume = πrrh = 22/7 * 7* 7 *7/2 = 11*49 = 539 cm³
Description : Find the total surface area of a hemisphere of radius 10 cm -Maths 9th
Last Answer : Radius of hemisphere, r = 10cm Formula: Total surface area of hemisphere = 3πr2 = 3×3.14×102 = 942 The total surface area of given hemisphere is 942 cm2.
Description : Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m -Maths 9th
Last Answer : Radius of cone, r = 24/2 m = 12m Slant height, l = 21 m Formula: Total Surface area of the cone = πr(l+r) Total Surface area of the cone = (22/7)×12×(21+12) m2 = 1244.57m2
Description : Two cubes of edge 6 cm are joined to form a cuboid. Find the total surface area of the cuboid. -Maths 9th
Last Answer : When two cubes are joined end to end, then Length of the cuboid = 6 + 6 = 12 cm Breadth of the cuboid = 6 cm Height of the cuboid = 6 cm Total surface area of the cuboid = 2 (lb + bh + hi) = 2(12 x6 + 6×6 + 6×12) = 2(72 + 36 + 72) = 2(180) = 360 cm2
Description : The total surface area of a cone whose radius is r/2 and slant height 2l is -Maths 9th
Last Answer : Total surface area of cone = πr(r+l) Given, radius = r/2 and slant height = 2l Therefore, new total surface area of cone = πr/2(r/2+2l) = π(r/4^2+rl) = πr(l+r/4)
Last Answer : Radius (r)=r/2 & slant height=2l TSA (S)=PIE R (l+r) =22/7×r/2(2l+r/2) =11/7×r(2l+r/2)
Description : Find the total surface area of a -Maths 9th
Last Answer : Total surface area of the cone = π(r/2)(2l + r/2) = πr( l + r/4).
Description : A solid cylinder has total surface area of 462 cm square. -Maths 9th
Last Answer : Let r cm be the radius of the base and h cm be the height of the cylinder, Then, total surface area of cylinder = 2 πr (r + h) Curved surface area of cylinder = 2 πrh We have, Curved surface area = 1/3(Total surface ... x 22 = 7/2 cm Volume of the cylinder = πr2h = 22/7 x 7 x 7 x 7/2 = 539 cm3
Description : 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
Description : The volume of a certain rectangular solid is 8 cm^3. Its total surface area is 32 cm^2 and its three dimensions are in geometric progression. -Maths 9th
Last Answer : (b) 32 Let the edges of the solid be a, ar, ar2. Then, Volume = a x ar x ar2 = a3r3 = (ar)3. Given (ar)3 = 8 ⇒ ar = 2 Also, surface area = 2(a x ar + ar x ar2 + a × ar2) = 2(a2r + ... Given, 2ar (a + ar + ar2) = 32 ⇒ 4(a + ar + ar2) = 32 ; Sum of lengths of all edges = 32.
Description : The magnitude of the volume of a closed right circular cylinder of unit height divided by the magnitude of the total surface area of the -Maths 9th
Description : 50 circular plates each of radius .... Find its total surface area -Maths 9th
Last Answer : 50 circular plate diameter of plate =14cm Radius of plate = d/2=214=7cm thickness =0.5cm → Height of the cylinder = No. of plates × thickness of plate =50×0.5 =25cm → total surface Area = curved surface + 2 × area of base =2πr.h+2×πr2 =2πr(h+r) =2π×7(25+7) =2×722×7×32 =1408cm2
Description : If the base of right rectangular prism remains constant and the measures of the lateral edges are halved, then its volume will be reduced by : -Maths 9th
Description : Calculate the edge of the cube if its volume is 1331 cm3 -Maths 9th
Last Answer : Let the edge of the cube be a Volume of a cube = a×a×a 1331= a×a×a 11 =a ( as 1331 is the cube of 11 Therefore , Edge of a cube is 11 cm