Question

If the height is 9 units and the volume is 36 cubic units, what is the surface area of a right circular cylinder?

Answer 1

44π square units.

Explanation:

The volume

36 = π r^2 h

36 = 9π r^2

π r^2 = 36/9 = 4π ( = the area of the base).

Now r^2 = 4

and r = 2.

So the circumference of the base = 2 * π * 2.

= 4π.

The area of the curve surface = 9 * 4π

= 36π.

The surface are of the cylinder = 2 * area of the base + area of the curved surface

= 2 * 4π + 36π

= 44π square units.

Answer 2

Volume

36π = πr^2*(9) ; Divide both sides by π and 9

4 = r^2 ; Take the square root of both sides

2 = r

Surface area

= 2π(2)(9) + 2π(2)^2

= 4π(9) + 2π(4)

= 36π + 8π

= 44π