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Mensuration

Short Answer Type

61. Find the volume of the following cuboids.

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62. Find the volume of the following cubes.
(a) with a side 4 cm (b) with a side 1.5 m.

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Long Answer Type

63.
A company sells biscuits. For packing purpose they are using cuboidal boxes:
box A $rightwards arrow$ 3 cm x 8 cm x 20 cm, box B $rightwards arrow$ 4 cm x 12 cm x 10 cm. What size of the box will be economical for the company? why? Can you suggest any other size (dimensions) which has the same volume but is more economical than these?

Clearly, Volume of box B = Volume of box A, but its surface area is less, so its more economical for the company.
Another size: 8 cm x 6 cm x 10 cm
∵ Volume = 8 x 6 x 10 cm³ = 480 cm³ Surface area = 2[(8 x 6) + (6 x 10) + (8 x 10)] cm²
= 2[48 + 60 + 80] cm²
= 2[188] cm² = 376 cm²
Since its surface area is still less than the box B.
∴ It is more economical for the company.

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Short Answer Type

64. Find the volume of the following cylinders.

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65.

Given a cylindrical tank, in which situation will you find surface area and in which situation volume.
(a) To find how much it can hold.
(b) Number of cement bags required to plaster it.
(c) To find the number of smaller tanks that can be filled with water from it.

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66. Find the height of a cuboid whose base area is 180 cm² and volume is 900 cm³.

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67. A cuboid is of dimensions 60 cm X 54 cm x 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?

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68. Find the height of the cylinder whose volume is 1.54 m³ and diameter of the base is 140 cm?

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69.

A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in litres that can be stored in the tank?

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70.

If each of a cube is doubled,
(i) How many times will its surface area increase?
(ii) How many times will its volume increase?

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