Question

Find the radius of the cylinder. Round your answer to the nearest millimeter.A. 4 mmB. 5 mmC. 8 mmD. 16 mm

Answer 1

A. 4 mm

Explanation

the volume of a cylinder is given by:

$Volume=\pi r^2h$

so

Step 1

a)let

$\begin{gathered} Volume=502.4\text{ mm}^3 \\ height=10\text{ mm} \end{gathered}$

b) now, replace in the formula and solve for r

$\begin{gathered} Volume=\pi r^2h \\ 502.4\text{ mm}^3=\pi r^2(10\text{ mm\rparen} \\ divide\text{ both sides by 10 mm} \\ \frac{502.4(mm)^3}{10\text{ mm}}=\frac{\text{ }\pi r^2(10mm\operatorname{\rparen}}{10\text{ mm}} \\ 50.24\text{ mm}^2=\pi r^2 \\ divide\text{ both sides by }\pi \\ \frac{50.24(mm)^2}{\pi}=\pi\frac{r^2}{\pi} \\ 15.99\text{ mm}^2=r^2 \\ square\text{ root in both sides} \\ \sqrt{15.99(mm)^2}=\sqrt{r^2} \\ 3.99\text{ mm}=r \\ r=4\text{ mm} \end{gathered}$

so, the radius is

A. 4 mm

I hope this helps you