Question

a sphere of diameter 15.6 cm is melted and cast into a right circular cone of height 31.2 cm find the diameter of the base of the cone

Answer 1

Answer: Diameter of cone is  7.8 cm

Step-by-step explanation:

Since we have given that

Diameter of sphere = 15.6 cm

Radius of sphere = 7.8 cm

Height of cone = 31.2 cm

Since a sphere is melted and cast into a right circular cone .

So, their volumes will be equal.

So, it becomes,

Volume of cone = Volume of sphere

$\frac{1}{3}\pi r^2h=\frac{4}{3}\pi r^3\\\\r^2\times 31.2=7.8\times 7.8\times 7.8\\\\r^2=15.21\\\\r=\sqrt{15.21}=3.9\ cm$

Diameter of cone is 2×3.9= 7.8 cm