Question

find the surface area and volume of the solid. round each measure to the nearest tenth, if necessary. volume: surface area:

Explanation:

Step1: Recall cone volume formula

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$, where $r$ is the radius and $h$ is the height.

Step2: Recall cone surface - area formula

The surface - area formula of a cone is $A = \pi r(r + l)$, where $r$ is the radius and $l$ is the slant height.

Step3: Identify values from the figure

Assume the radius $r = 5$ ft and the slant height $l=13.6$ ft and height $h$ (not given in the description part of your input, assume we calculate it using $l^{2}=h^{2}+r^{2}$, so $h=\sqrt{l^{2}-r^{2}}=\sqrt{13.6^{2}-5^{2}}=\sqrt{184.96 - 25}=\sqrt{159.96}\approx12.64$ ft).

Step4: Calculate volume

$V=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi\times5^{2}\times12.64=\frac{1}{3}\pi\times25\times12.64\approx329.9$ cubic - feet.

Step5: Calculate surface area

$A=\pi r(r + l)=\pi\times5\times(5 + 13.6)=5\pi\times18.6\approx292.0$ square - feet.

Answer:

Volume: approximately $329.9$ cubic - feet
Surface area: approximately $292.0$ square - feet