Question

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

Explanation:

Step1: Calculate the volume of the cone

The formula for the volume of a cone is $V=\frac{1}{3}\pi r^{2}h$. Given $r = 5m$ and $h=17m$, we substitute these values into the formula: $V=\frac{1}{3}\pi\times5^{2}\times17=\frac{1}{3}\pi\times25\times17=\frac{425\pi}{3}\approx445.05m^{3}$.

Step2: Calculate the slant - height of the cone

The slant - height $l$ of a cone is calculated using the Pythagorean theorem $l=\sqrt{r^{2}+h^{2}}$. Substituting $r = 5m$ and $h = 17m$, we get $l=\sqrt{5^{2}+17^{2}}=\sqrt{25 + 289}=\sqrt{314}\approx17.72m$.

Step3: Calculate the surface area of the cone

The formula for the surface area of a cone is $A=\pi r(r + l)$. Substituting $r = 5m$ and $l\approx17.72m$, we have $A=\pi\times5\times(5 + 17.72)=5\pi\times22.72\approx357.08m^{2}$.

Answer:

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