If a sphere and a cube have equal surface areas.

If a sphere and a cube have equal surface areas, then the ratio of the diameter of the sphere to the edge of the cube is
(a) 1: 2
(b) 2: 1
(c) √π: √6
(d) √6: √π

Solution:

A sphere and a cube have equal surface area
Let a be the edge of a cube and r be the radius of the sphere, then

A solid piece of iron in the form of a cuboid of dimensions 49 cm x 33 cm x 24 cm is moulded to form a sphere. The radius of the sphere is
(a) 21 cm
(b) 23 cm
(c) 25 cm
(d) 19 cm

Solution:

Dimension of a cuboid = 49 cm × 33 cm × 24 cm
Volume of a cuboid = 49 × 33 × 24 cm³
⇒ Volume of sphere = Volume of a cuboid
Volume of a sphere = 49 × 33 × 24 cm³

More Solutions:

• Then the number of marbles that the cube can accommodate.
• Find the cost of the tin for making the container.
• Find the volume and the total surface area of a cone.
• Find the capacity of the bowl.
• A solid wooden toy is in the shape of a right circular cone.
• Find the volume and the total surface area of the solid.