Question

find the volume and surface area of the cone if the height is 17m and the radius is 5m

Explanation:

Step1: Calculate the slant height $l$

Use the Pythagorean theorem $l=\sqrt{h^{2}+r^{2}}$, where $h = 17$ and $r = 5$.
$l=\sqrt{17^{2}+5^{2}}=\sqrt{289 + 25}=\sqrt{314}\approx17.72$

Step2: Calculate the volume $V$ of the cone

The formula for the volume of a cone is $V=\frac{1}{3}\pi r^{2}h$.
$V=\frac{1}{3}\pi\times5^{2}\times17=\frac{425\pi}{3}\approx445.05$ $m^{3}$

Step3: Calculate the surface - area $A$ of the cone

The formula for the surface area of a cone is $A=\pi r(r + l)$.
$A=\pi\times5\times(5 + 17.72)=5\pi\times22.72\approx357.08$ $m^{2}$

Answer:

Volume: $\frac{425\pi}{3}\approx445.05$ $m^{3}$, Surface Area: $5\pi\times22.72\approx357.08$ $m^{2}$