Question

A cone has a volume of 144 cube in and a diameter of 12 in. Wilson states that a cylinder with the same height and diameter has the same volume. Which statementexplains whether or not Wilson is correct?O A cylinder in which h = 12 and d = 12 has a volume of 144pi in3; therefore, Wilson is correct.O A cylinder in which h = 4 and d = 12 has a volume of 144pi in3; therefore, Wilson is correct.O A cylinder in which h= 12 and d = 12 has a volume of 432pi in3; therefore, Wilson is incorrect.O A cylinder in which h = 4 and d = 12 has a volume of 432pi in3; therefore, Wilson is incorrect.

Answer 1

Step 1

State the formula for the volume of a cone

$V=\frac{1}{3}\pi r^2h$

where;

$\begin{gathered} \pi=3.14 \\ r=\frac{diameter}{2}=\frac{12}{2}=6 \\ v=144in^3 \end{gathered}$

Step 2

Find the height of the cone.

$\begin{gathered} v=\frac{1}{3}\pi r^2h \\ 144=\frac{1}{3}\pi(6)^2(h) \\ 144=\frac{1}{3}\pi(36)(h) \\ 144=12\pi h \\ \frac{12\pi h}{12\pi}=\frac{144}{12\pi} \\ h=\frac{12}{\pi}in \end{gathered}$

Step 3

Consider the options and dechipher the answer.

$\text{The volume of a cylinder=}\pi\text{r}^2h$$undefined$