Question

a sphere has a radius of 3 inches and a density of 82 ounces per cubic inch. what is the mass, in ounces, of the sphere?

a 188/40

b 418/18

c 246π

d 2,952π

Explanation:

Step1: Calculate the volume of the sphere

The volume formula for a sphere is \(V=\frac{4}{3}\pi r^{3}\). Given \(r = 3\) inches, substitute into the formula:
\(V=\frac{4}{3}\pi(3)^{3}=\frac{4}{3}\pi\times27 = 36\pi\) cubic inches.

Step2: Use the density - mass - volume relationship

The formula is \(m=
ho V\) (where \(m\) is mass, \(
ho\) is density, and \(V\) is volume). Given \(
ho = 82\) ounces per cubic inch and \(V = 36\pi\) cubic inches.
Then \(m=82\times36\pi\).
Calculate \(82\times36=(80 + 2)\times36=80\times36+2\times36=2880+72 = 2952\).
So \(m = 2952\pi\) ounces.

Answer:

D. \(2,952\pi\)