Q 4. - Calculus

Question

Give formulas for the volume and the surface area of a cone with radius $u$ and height $w$.

Step-by-Step Solution

Answer

Volume of cone is $V=\frac{1}{3}\pi u^{2}w$.

Surface area of cone is $S=\pi u\sqrt{u^2+w^2}+\pi u^2$.

Step 1. Standard formulas

The volume and surface area of a right circular cone of radius $r$ and height $h$ are

$V=\frac{1}{3}\pi r^{2}h$

$S=\pi r\sqrt{r^2+h^2}+\pi r^2$

Step 2. Substitution and solution

Now given that radius is $u$ and height is $w$ of cone

Substitute in standard formulas we get,

Volume of cone is $V=\frac{1}{3}\pi u^{2}w$.

Surface area of cone is $S=\pi u\sqrt{u^2+w^2}+\pi u^2$.