Question

a manufacturer makes decorative globes out of silver in the shape of a solid sphere. suppose each sphere has a radius of 4.5 cm. if silver is priced at $5.00 per cm^{3}, how much will the silver cost to make one solid sphere? use 3.14 for π, and do not round your answer.

Explanation:

Step1: Calculate the volume of the sphere

The volume formula of a sphere is $V = \frac{4}{3}\pi r^{3}$. Given $r = 4.5\ cm$ and $\pi=3.14$.

$$\begin{align*} V&=\frac{4}{3}\times3.14\times(4.5)^{3}\\ &=\frac{4}{3}\times3.14\times91.125\\ & = 4\times3.14\times30.375\\ &=381.51\ cm^{3} \end{align*}$$

Step2: Calculate the cost of the silver

Since silver is priced at $\$5.00$ per $cm^{3}$, and the volume of the sphere is $V = 381.51\ cm^{3}$. The cost $C=5\times V$.
$$C = 5\times381.51=\$1907.55$$

Answer:

$\$1907.55$