Diameter

Volume of cone=pi. r^2. h/3

144pi =pi x r^2 x [12/3] divide both sides by 4pi

36=r^2 take the square root of both sides.

r=6 inches-the radius of its base

6 x 2=12 inches- the diameter of the base.

The volume of a cone w a height of 12 in. is 144pi cubic inches.

What is the length in inches, of the diameter of its base?

$h_{\text{cone}} = 12\ in.\\ V_{\text{cone}} = 144\cdot \pi\ in^3 \\ d_{\text{cone}} = 2\cdot r \\ r = radius$

$\begin{array}{rcll} \frac13 \cdot \pi \cdot r^2 \cdot h &=& V_{\text{cone}} \qquad &| \qquad h = 12 \quad V=144\cdot \pi\\ \frac13 \cdot \pi \cdot r^2 \cdot 12 &=& 144\cdot \pi \qquad &| \qquad :\pi \\ \frac13 \cdot r^2 \cdot 12 &=& 144 \qquad &| \qquad 144 = 12\cdot 12 \\ \frac13 \cdot r^2 \cdot 12 &=& 12\cdot 12 \qquad &| \qquad : 12 \\ \frac13 \cdot r^2 &=& 12 \qquad &| \qquad \cdot 3 \\ r^2 &=& 12 \cdot 3 \\ r^2 &=& 36 \qquad &| \qquad 36= 6\cdot 6 \\ r^2 &=& 6\cdot 6 \\ r^2 &=& 6^2 \qquad &| \qquad \sqrt{()} \\ r &=& 6 \\\\ d &=& 2\cdot r \\ d &=& 2\cdot 6 \\ \mathbf{ d }& \mathbf{=} & \mathbf{12\ in.} \end{array}$

The diameter of its base is 12 in.