Answer
a. $$57,300\ m^3 .$$
b. $$6380\ m^2 .$$
Work Step by Step
a. The volume of the cone is given by
$$ V=\frac{1}{3} \times base \ area \times altitude = \frac{1}{3} \pi (37.6^2)(38.7)=57294.8\ m^3 \approx 57,300\ m^3 .$$
b. The slant height of the cone is given by
$s=\sqrt{38.7^2+37.6^2}=53.96\ m$
The lateral surface area is given by
$$ Surface \ area= \pi r s=\pi (37.6) (53.95)=6372.78\ m^2\approx 6380\ m^2 .$$
