Answer to Question #170441 in Geometry for Leighton

Question

For a solid cylinder of radius r and height h:

(i) write down the expression for the total surface area A,

(ii) write down the expression for the volume V,

(iii) using these expressions express V in terms of A and r in its simplest

form.

Answer 1

(i)

$$A=2\pi rh+2\pi r^2$$

(ii)

$$V=\pi r^2h$$

(iii)

$$h=\dfrac{A-2\pi r^2}{2\pi r}$$

$$V=\dfrac{r(A-2\pi r^2)}{2}$$