Question

what is the volume of this cone? round your answer to the nearest hundredth. 16 cm 12 cm cubic centimeters

Explanation:

Step1: Find the height of the cone using Pythagorean theorem

Let the slant - height $l = 16$ cm and the radius $r = 12$ cm. By the Pythagorean theorem $h=\sqrt{l^{2}-r^{2}}$, where $h$ is the height of the cone. So $h=\sqrt{16^{2}-12^{2}}=\sqrt{(16 + 12)(16 - 12)}=\sqrt{28\times4}=\sqrt{112}=4\sqrt{7}$ cm.

Step2: Use the volume formula for a cone

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 12$ cm and $h = 4\sqrt{7}$ cm into the formula. $V=\frac{1}{3}\pi\times12^{2}\times4\sqrt{7}=\frac{1}{3}\pi\times144\times4\sqrt{7}=192\sqrt{7}\pi$ $cm^{3}$.

Step3: Calculate the numerical value and round

$V = 192\sqrt{7}\pi\approx192\times2.64575\times3.14159\approx1596.18$ $cm^{3}$.

Answer:

$1596.18$