Question

An oatmeal container has a diameter of 9 inches and a volume of 239.4 in3. What is the lateral surface area of the oatmeal container? Hint: You have to use the Volume to find the height before you can calculate the lateral surface area. Round your answer to the nearest tenth.

Answer 1

Lateral surface area = 106.4
`in^(2)`.

Explanation:

Assumed that the oatmeal container has the shape of a cylinder. Its lateral surface area can be determined by:

lateral surface area = 2
`\pi`rh

But,

volume =
`\pi`
`r^(2)`h

where: r is the radius, and h is the height.

From the question, volume = 239.4
`in^(3)`, and diameter = 9 inches, then;

radius =
`(diameter)/(2)` =
`(9)/(2)`

= 4.5

radius = 4.5 inches

Thus,

volume =
`\pi`
`r^(2)`h

239.4 =
`\pi`x
`(4.5)^(2)` x h

= 20.25
`\pi`h

h =
`(239.4)/(20.25\pi )`

=
`(11.8222)/(\pi )`

h =
`(11.8222)/(\pi )` inches

Therefore,

lateral surface area = 2
`\pi`rh

= 2
`\pi`(4.5)(
`(11.8222)/(\pi )`)

= 2 x 4.5 x 11.8222

= 106.3998

Lateral surface area of the oatmeal container is 106.4
`in^(2)`.