Question

A manufacturer makes decorative globes out of silver in the shape of a solid sphere. Suppose each sphere has a radius of 1.5cm. If silver is priced at $8.00 per, how much will the silver cost to make one solid sphere?

Use 3.14 for
`\pi` , and do not round your answer.

Answer 1

• Radius=1.5cm

Volume

• 4/3πr³
• 4/3π(1.5)³
• 4/3π(3.375)
• 4.5π
• 14.13cm³

Cost per cm³=$8

Total cost

• 14.13(8)
• $113.04

Answer 2

$113.04

Explanation:

Formula

`\sf \textsf{Volume of a sphere}=\frac43 \pi r^3 \quad \textsf{(where r is the radius)}`

`\begin{aligned}\textsf{Given}: \quad \sf r & =\sf 1.5\:cm\\ \pi & = \sf 3.14 \end{aligned}`

`\begin{aligned}\implies \sf \textsf{Volume of silver globe} & =\sf \frac43 \cdot 3.14 \cdot (1.5)^3\\\\& =\sf 14.13 \:cm^3\end{aligned}`

`\textsf{Given}: \quad \sf Cost\:of\:silver=\$ 8.00\:per\:cm^3`

`\begin{aligned}\implies \textsf{Cost of silver for one globe} & =\textsf{Volume of globe} * \sf \$ 8.00\\ & =\sf 14.13 * \sf \$ 8.00\\& =\sf \$ 113.04\end{aligned}`