Question

The dimensions of a metallic cuboid are 44 cm × 42 cm × 21 cm. it is molten and recast into a sphere. Find the surface area of the sphere.

Answer 1

The volume of cuboid = l × b × h

                                    = (44 × 42 × 21) cm³

                                     = 38808 cm³

Since, the metallic cuboid is molten and into a sphere, 

volume of sphere = volume of cuboid 

∴ volume of sphere = 38808 cm³

But, volume of sphere = `4/3 pir^3`

∴  `4/3 pir^3` = 38808

∴ `r^3 = 38808 xx 3/4 xx 7/22`

∴  r³ = 21 × 21 × 21 

∴ r = 21 cm 

∴ surface area of spher = 4πr²

                                      = `4 xx 22/7 xx(21)^2`

                                      = 5544 cm²

∴ the surface area of the sphere is 5544 cm².