Question

If a solid right circular cone of height 24 cm and base radius 6 cm is melted and recast in the shape of a sphere then the radius of the sphere is
a)6 cm
b) 4 cm
c)8 cm
d)12 cm

Answer 1

radius of sphere is 6cm.

Answer 2

The radius of the sphere is 6 cm

Step-by-step explanation:

Height of cone = 24 cm

Radius of cone = 6 cm

Volume of cone =$\frac{1}{3} \pi r^2 h = \frac{1}{3} \pi \times 6^2 \times 24$

We are given that a solid right circular cone of height 24 cm and base radius 6 cm is melted and recast in the shape of a sphere

So, Volume of cone = Volume of sphere

$\frac{1}{3} \pi \times 6^2 \times 24=\frac{4}{3} \pi r^3$

6^2 \times 24=4 r^3

$\sqrt[3]{\frac{6^2 \times 24}{4}}=r$

6=r

Hence the radius of the sphere is 6 cm

#Learn more:

A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm.

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