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Surface Areas and Volumes

Short Answer Type

461. Two cylindrical cans have equal base areas. The diameter of each is 56 cm. If one of the can is 15 cm high and the other is 20 cm high, find the ratio of their volumes.

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462.

The radii of two cylinders are in the ratio 4 : 3. Find the ratio of their volumes, if the heights are taken to be the same.

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463. The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. Find the ratio of their volumes.

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464. The ‘volumes’ of two cones are in the ratio 2:3 and the ratio between their radii is also 2:3 Find the ratio between their heights.

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465. The volumes of two right circular cones are in the ratio 3:5 and their heights are in the ratio 5:3. Find the ratio between their radii.

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466. The height and base of cone each is increased by 100% what is the ratio between the volume of a given cone and new cone.

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467. Find the depth of a cylindrical tank of radices 28 m, if its capacity is equal to that of a rectangular tank of size 28m x 16m x 11m..

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468. A metallic sphere 1 dm in diameter is beaten into a circular sheet of uniform thickness equal to 1 mm. Find the radius of the sheet.

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469. Two cubes each of 10 cm edge are joined end to end. Find the surface area of the resulting cuboid.

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470. Three cubes each of side 5 cm are joined end to end. Find the Surface Area of the resulting cuboid.

Let l, b and h are respectively the length, breadth and height of the cuboid, then
l = (5 + 5 + 5) cm = 15 cm
when three cubes are joined we get a cuboid
b = 5 cm and h = 5 cm.
Now,
The Surface Area of the resulting cuboid
= 2 (lb + bh + hl) cm²= 2 (15 x 5 + 5 x 5 + 5 x 15) cm²= 2 (75 + 25 + 75) cm²= 2 (175) cm²= 350 cm².

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