Question

A cylinder has a height that is 2 times as large as its radius. The lateral area of the cylinder is 16π square units. What is the length of the radius of the cylinder?

(please show work)

Answer 1

Answer: 2 units

Explanation:

The lateral area of the cylinder is given by :-

`L.A.=2\pi r h`, where r is radius and h is the height of cylinder.

Given: The lateral area of the cylinder = 16π square units.

Let r be the radius of the triangle, then we have

Height of cylinder = 2r

The lateral area of the given cylinder will be :-

`16\pi=2\pi r(2r)\\\\\Rightarrow2r^2=8\\\\\Rightarrow r^2=4\\\\\Rightarrow r=\pm2`

Hence, the length of the radius of the cylinder = 2 units.

Answer 2

The length of the radius of the cylinder is 2 units.

The lateral surface area of a cylinder = 2πrh
where, r = base radius
h = height of cylinder
Now, height of cylinder = 2r units

⇒ 16 π = 2×π×r×h
⇒ 16 π = 2×π×r×2r
⇒
`r^(2)` = 4
⇒ r = 2 units
Thus, radius is 2 units.