Question

A perfectly spherical scoop of ice cream has a surface area of 36π cm2 and the same diameter as the open end of the ice cream cone it rests on. The cone is 11 cm tall. If the ice cream melts into the cone, what volume of ice cream will overflow?

Answer 1

9.43 cm³

Explanation:

Given that the surface area of the spherical scoop is 36π cm², we find its radius. The surface area of a sphere, A = 4πr² where r = radius

36π cm² = 4πr²

r² = 36π cm²/4π

r² = 9 cm²

r = √(9 cm²)

r = 3 cm

So, the volume of the spherical scoop of ice cream is thus V = 4πr³/3

= 4π(3 cm)³/3

= 4π(9 cm³)

= 36π cm³

The volume of the ice cream cone is V' = πr²h/3 where r = radius of cone = radius of spherical scoop = 3cm and h = height of cone = 11 cm

V' = π(3 cm)² × 11 cm/3

= 9π cm² × 11 cm/3

= 33π cm³

So, the volume of ice cream that will overflow is thus V - V' = 36π cm³ - 33π cm³

= 3π cm³

= 9.43 cm³