Question

A sphere is melted and recast into 8 identical cones, each with radius 3 cm and height 4 cm. What was the radius of the original sphere?

• A. 4.16 cm
• B. 5.28 cm
• C. 4.32 cm
• D. 6.12 cm

Answer 1

Answer:

A. 4.16 cm

Since the sphere is melted and recast, volume remains the same.

Step 1: Volume of 1 cone

$V=\frac13\pi r^2h$

Given (r=3) cm and (h=4) cm:

$V=\frac13\pi(3)^2(4)=12\pi\text{ cm}^3$

For 8 cones:

$8\times12\pi=96\pi\text{ cm}^3$

Step 2: Volume of the sphere

$\frac43\pi R^3=96\pi$

Cancel $(\pi):$

$\frac43R^3=96$

$R^3=72$
$R=\sqrt[3]{72}\approx4.16$

Answer: The radius of the sphere is approximately$(\boxed{4.16\text{ cm}}).$