Mensuration Volume and Area Practice Questions with Detailed Solution Level - 1

If V be the volume and S be the surface area of a cuboid of dimensions a, b, c, then 1/V is equal to

It is required to construct a big rectangular hall to accommodate 500 persons, allowing 22.5 m³ space per person. The height of the hall is to be kept at 7.5 m, while the total inner surface area of the walls must be 1200 sq. m. Then the length and breadth of the hall respectively are

A rectangular tank measuring 5 m × 4.5 m × 2.1 m is dug in the centre of the field measuring 13.5 m by 2.5 m. The earth dug out is evenly spread over the remaining portion of the field. How much is the level of the field raised?

The length, breadth and height of a cuboid are in the ratio 1 : 2 : 3. The length, breadth and height of the cuboid are increased by 100%, 200% and 200% respectively. Then the increase in the volume of the cuboid is

If a metallic cuboid weighs 16 kg, how much would a miniature cuboid of metal weigh, if all dimensions are reduced to one-fourth of the original?

A rectangular water tank is open at the top. Its capacity is 24 m³. Its length and breadth are 4 m and 3 m respectively. Ignoring the thickness of material used for building the tank, the total cost of painting the inner and outer surfaces of the tank at the rate of ₹10 per m² is

If the areas of three adjacent faces of a cuboid are x, y, z respectively, then the volume of the cuboid is

The length of an edge of a hollow cube open at one face is √3 metres. What is the length of the largest pole that it can accommodate?

If the total length of diagonals of a cube is 12 cm, then what is the total length of the edges of the cube?

A larger cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. The ratio of the total surface areas of the smaller cubes and the larger cube is