If a right circular cone of height 24 cm has a volume of 1232 cm³, then the area (in cm²) of curved surface area is

• 550

• 704

• 924

• 924

If each edge of a cube is increased by 50%, the percentage increase in surface area is

• 125%

• 50%

• 100%

• 100%

If the surface areas of two spheres are in the ratio 4 : 9, then the ratio of their volumes will be

• 4 : 9

• 16 : 27

• 8 : 27

• 8 : 27

A rectangular block of metal has dimensions 21 cm, 77 cm and 24 cm. The block has been melted into a sphere. The radius of the sphere is

• 21 cm

• 7 cm

• 14 cm

• 14 cm

A right circular cone is 3.6 cm high and radius of its base is 1.6 cm. It is melted and recast into a right circular cone with radius of its base as 1.2 cm. Then the height of the cone (in cm) is

• 3.6

• 4.8

• 6.4

• 6.4

If h, c, v are respectively the height, curved surface area and volume of a right circular cone, then the value of  is

• 2

• -1

• 1

• 1

47.

Assume that a drop of water is spherical and its diameter is one-tenth of a cm. A conical glass has a height equal to the diameter of its rim. If 32,000 drops of water fill the glass completely, then the height of the glass, in cm, is

• 1

• 2

• 3

• 3

The volume of a conical tent is 1232 cu.m and the area of its base is 154 sq.m. Find the length of the canvas required to build the tent, if the canvas is 2m in width.

• 270 m

• 272 m

• 276 m

• 276 m

The total number of spherical bullets, each of diameter 5 decimeter, that can be made by utilizing the maximum of a rectangular block of lead with 11 metre length, 10 metre breadth and 5 metre width is (assume that  > 3).

• equal to 8800

• less than 8800

• equal to 8400

• equal to 8400

The heights of a cone, cylinder and hemisphere are equal. If their radii are in the ratio 2 : 3 : 1, then the ratio of their volume is

• 2 : 9 : 2

• 4 : 9 : 1

• 4 : 27 : 2

• 4 : 27 : 2