Question

Find the volume of the sphere. Either enter an exact answer in terms of ar or use 3.14 for pi and round your final answer to the nearest hundredth.

Answer 1

Volume of a sphere

We have a sphere of radius 4

r = 4

We know that the equation for the volume is:

$V=\frac{4}{3}\pi r^3$

We know that:

r = 4

and

π = 3.14

Then, we replace in the equation:

$\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \downarrow \\ V=\frac{4}{3}\cdot3.14\cdot4^3 \end{gathered}$

Since

4³ = 64

then

$\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot4^3 \\ =\frac{4}{3}\cdot3.14\cdot64 \\ =267.9467 \\ =\frac{4}{3}\cdot\pi\cdot64=\frac{256}{3}\pi \end{gathered}$

We want to round our answer to the nearest hundredth (two numbers after the decimal point).

For this case we have two options:

267.94 or 267.95

Since

267.9500 is nearer to 267.9467

than

267.9400

then the answer is 267.95

Answer: the volume of the sphere is 267.95 units³ or (256/3)π units³