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 : 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 : A metallic sheet is of rectangular shape with dimensions 48 cm x 36 cm. From each of its corners, a square of 8 cm is cut-off and an open box is made of the remaining sheet. Find the volume of the box. -Maths 9th
Last Answer : When squares of 8 cm is cutt-off from rectangulare sheet then, Length of box (l) = (98 - 8 - 8) = 32 cm Breadth of box (b) = (36 - 8 - 8) = 20 cm Height of box (h) = 8cm ∴ Volume of box = lbh = 32 x 20 x 8 = 5120 cm3
Description : If two rectangular sheets each of dimensions 2x and 2y form the curved surfaces of two different cylinders, then the ratio -Maths 9th
Last Answer : answer:
Description : The total surface area of a cube is 96 cm2 . The volume of the cube is -Maths 9th
Last Answer : NEED ANSWER
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.
Description : A metallic sheet is of rectangular shape with dimensions 28m × 36m. From each of its corners, a square is cut off so as to make an open box. -Maths 9th
Last Answer : R.E.F image Volume of box =l×b×h From the diagram l=48−2(8) ∵ Two square formed side =32m b=36−2(8) =20m Also h=8m from question ∴ Volume =32×20×8 =5120m3
Description : A design is made on a rectangular tile of dimensions 50 cm x 17 cm as shown in figure. -Maths 9th
Last Answer : According to question find the the total area of the design and the remaining area of the tiles.
Description : Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm x 8 cm x 8 cm. -Maths 9th
Last Answer : Volume of rectangular box=lbh=16(64)=1024cm3 Volume of sphere=34πr3=33.5238cm3 16 sphere=16(33.5238)=536.3808 Volume of liquid=1024−536.3808=488cm3
Last Answer : According to question find the volume of this liquid.
Description : A rectangular box has dimensions x, y and z units, where x < y < z. If one dimension is only increased by one unit, -Maths 9th
Description : Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find (i) radius of the base -Maths 9th
Last Answer : Slant height of cone, l = 14 cm Let the radius of the cone be r. (i) We know, CSA of cone = πrl Given: Curved surface area of a cone is 308 cm2 (308 ) = (22/7) r 14 308 = 44 r r = 308 ... Total surface area of cone = 308+(22/7) 72 = 308+154 Therefore, the total surface area of the cone is 462 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 curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder. (Assume π =22/7 ) -Maths 9th
Last Answer : Height of cylinder, h = 14cm Let the diameter of the cylinder be d Curved surface area of cylinder = 88 cm2 We know that, formula to find Curved surface area of cylinder is 2πrh. So 2πrh =88 cm2 (r is the ... 88 cm2 2r = 2 cm d =2 cm Therefore, the diameter of the base of the cylinder is 2 cm.
Description : The curved surface area of a cylinder is 154 cm2. -Maths 9th
Last Answer : Since curved surface area of a cyclinder = 154 cm2 [given] Total surface area of cyclinder = 3 curved surface area 2πrh + 2πr2 = 3 154 154 + 2πr2 = 462 2πr2 = 462 - 154 = 308 r2 = 308 7 / 2 22 = 49 ... 154 / 44 = 3.5 cm ∴ Volume of cyclinder = πr2h = 22 / 7 7 7 3.5 = 539 cm3
Description : what- possible side lengths for a rectangular frame are 6 inches, 10 inches, and 12 inches.If all measurements are whole numbers, which dimensions can be used to frame a picture that has an area between 45 and 50 square inches?
Last Answer : 6 in. by 8 in., 10 in. by 5 in., 12 in. by 4 in.
Description : what= possible side lengths for a rectangular fence are 8 feet, 10 feet, and 12 feet. Marsha wants to fence in an area between 90 and 130 square feet.If the measurements are whole numbers, what dimensions can Marsha use?
Last Answer : 8 ft. by 12 ft., 10 ft. by 10 ft., 12 ft. by 10 ft.
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 : 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 : 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 : 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
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 : If V is the volume of a cuboid of dimensions l, -Maths 9th
Last Answer : V = lbh and S = 2(lb + bh + hl) Now RHS = 2/S(1/l + 1/b + 1/h) = 2/S(bh + hl + lb/lbh) = 2/S x S/2 x 1/V = 1/V = LHS.
Description : An isosceles right triangle has area 8 cm2. The length of its hypotenuse is -Maths 9th
Last Answer : (a) Given, area of an isosceles right triangle = 8 cm2 Area of an isosceles triangle = 1/2 (Base x Height) ⇒ 8 = 1/2 (Base x Base) [∴ base = height, as triangle is an ... √32 cm [taking positive square root because length is always positive] Hence, the length of its hypotenuse is √32 cm.
Last Answer : This answer was deleted by our moderators...
Description : The area of a rhombus 10 cm2 .If one if its diagonal is 4 cm,then find the other diagonal. -Maths 9th
Last Answer : hope its clear
Description : An isosceles right triangle has area 8 cm2 . Find the length of its hypotenuse. -Maths 9th
Last Answer : Area = 1/2a2 ⇒ 1/2a2 = 8 ⇒ a2 = 16 cm ⇒ a = 4 cm Hypotenuse = √2a = √2.4 = 4√2 cm.
Description : A rectangular paper 11 cm by 8 cm can be exactly wrapped to cover the curved surface of a cylinder of height 8 cm . -Maths 9th
Description : The area of the parallelogram ABCD is 90 cm2. -Maths 9th
Last Answer : Given, area of parallelogram, ABCD = 90 cm2 1.We know that, parallelograms on the same base and between the same parallel are equal in areas. Here, parallelograms ABCD and ABEF are on same base AB and between the same parallels AB ... (ABEF) = 1/2 x 90 = 45 cm2 [∴ ar (ABEF) = 90 cm2, from part (i)]
Description : The area of a trapezium is 475 cm2 and the height is 19 cm. -Maths 9th
Last Answer : Let the length of one parallel side of trapezium is a. So length of other parallel side = a + 4 Given the area of trapezium = 475 & the height = 19 Now area of a trapezium = 21 height ... =23∴Length of smalle rparallel side of trapezium =23 & Length of other parallel side of trapezium = 23+4=27
Last Answer : According to question find the lengths of its two parallel sides
Description : PQRS is a parallelogram whose area is 180 cm2 and A is any point on the diagonal QS. The area of △ASR = 90 cm2. Find this statement is true or false. -Maths 9th
Last Answer : Solution :- As diagonal of the parallelogram divides it into two triangles of equal area. Since, area (△SRQ ) = 1/2 area(PQRS) area (△SRQ ) = 1/2 x 180 ... = 90 cm2 (Given) This is not possible unless area (△SRQ ) = area (△ASR ) So, the given statement is false.
Description : In Fig. 9.23, ABCD is a parallelogram in which BC is produced to E such A B that CE = BC. AE intersects CD at F. If area of △BDF = 3 cm2, find the area of parallelogram ABCD. -Maths 9th
Last Answer : Solution :-
Description : A hemispherical bowl has its external diameter equal to 10 cm and its thickness is 1 cm. What is the whole surface area of the bowl ? -Maths 9th
Last Answer : External radius of hemispherical bowl = 5 cm Internal radius of the bowl = (5 – 1) cm = 4 cm Surface area of external portion = 2π(5)2 = 50 p sq. cm Surface area of internal portion = 2π(4)2 = ... = 91π sq. cm = (91×227)(91×227) sq. cm = 13 × 22 sq. cm = 286 cm2
Description : (i) The base of an open rectangular box is square and its volume is ` 256 cm^(3)`. Find the dimensions of this box if we want to use least material fo
Last Answer : (i) The base of an open rectangular box is square and its volume is ` 256 cm^(3)`. ... dimensions of this window from which maximum light can admit.
Description : The paint in a certain container is sufficient to paint an area equal to 9.375 m2. How many bricks of dimensions 22.5 cm×10 cm×7.5 cm can be painted out of this container? -Maths 9th
Last Answer : Total surface area of one brick = 2(lb +bh+lb) = [2(22.5 10+10 7.5+22.5 7.5)] cm2 = 2(225+75+168.75) cm2 = (2 468.75) cm2 = 937.5 cm2 Let n bricks can be painted out by the ... 93750 cm2 So, we have, 93750 = 937.5n n = 100 Therefore, 100 bricks can be painted out by the paint of the container.
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 : 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
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 : From a wooden cylindrical block, whose diameter is equal to its height, a sphere of maximum possible volume is carved out. -Maths 9th
Description : case study questions class 9 maths surface area and volume -Maths 9th
Last Answer : Q. Read the source or text given below and answer the following questions: A conical circus tent has to be made with a cloth that is 5m wide, whose height is 24m, and the radius of the base is 7m. ... 4. Find the Curved Surface Area Answers: 1. Curved Surface Area 2. 550 m 3. Rs.3850 4.110m²
Description : A spherical ball is divided into two equal halves. If the curved surface area of each half is 56.57 cm?, find the volume of the spherical ball.11531/cylinder-radius-halved-and-height-doubled-then-find-volume-with-respect-original-volume -Maths 9th
Last Answer : since curved surface of half of the spherical ball = 56.57 cm2 ∴ 2πr2 = 56.57 ⇒ r2 = 56.57 / 2 × 3.14 = 9 ⇒ r = 3 cm Now, volume of spherical ball = 4 / 3 πr3 = 4 / 3 × 3.14 × 3 × 3 × 3 = 113.04 cm3