Question

a sphere has a radius of 9 inches. an artist creates a replica of the structure that has been scaled up by a factor of 1.5. what is the volume of the replica in in.³? 10,305.99 in.³ 9743.98 in.³ 8681.99 in.³ 11,184.98 in.³

Explanation:

Step1: Find the radius of the replica

The original radius is 9 inches and it is scaled up by a factor of 1.5. So the new radius $r = 9\times1.5=13.5$ inches.

Step2: Use the volume - formula for a sphere

The volume formula of a sphere is $V=\frac{4}{3}\pi r^{3}$. Substitute $r = 13.5$ into the formula:
\[

$$\begin{align*} V&=\frac{4}{3}\times\pi\times(13.5)^{3}\\ &=\frac{4}{3}\times\pi\times2460.375\\ &=4\times\pi\times820.125\\ &\approx4\times3.14\times820.125\\ & = 12.56\times820.125\\ &=10305.9 \end{align*}$$

\]

Answer:

10,305.99 in.$^{3}$