Question

A cylinder has a lateral surface area of 34 and a height of 6. What is the circumference of the base? Round to the nearest tenth.

Answer 1

Surface Area of Cylinder

The circumference of the base is 5.7

Explanation:

The lateral surface of an object is defined as the area of all the sides of the object, excluding the area of its base and top.

A cylinder has two faces, two curved edges where the curved wall meets the end circles, and a curved surface stretching between the two circular ends.

For a cylinder, the lateral surface area is the curved surface that connects the base and the top.

The lateral surface area
`A_(L) = 2\pi rh\\`

where r is radius of the base of the cylinder

and h is height of the cylinder

and
`\pi` is 3.14

The circumference of the base of cylinder = C

where C =
`2\pi r\\`

Given
`A_(L)\\` = 34 and h = 6

⇒
`A_(L)\\\\` = C × h

⇒
`C = (A_(L))/(h)`

⇒ C =
`(34)/(6)` = 5.7

Hence the circumference of the base of the cylinder is 5.7