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

Answer:

Lateral surface area = 106.4 $in^{2}$.

Step-by-step 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 = $\frac{diameter}{2}$ = $\frac{9}{2}$

          = 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 = $\frac{239.4}{20.25\pi }$

  = $\frac{11.8222}{\pi }$

h = $\frac{11.8222}{\pi }$ inches

Therefore,

lateral surface area = 2$\pi$rh

                                = 2$\pi$(4.5)($\frac{11.8222}{\pi }$)

                                = 2 x 4.5 x 11.8222

                                = 106.3998

Lateral surface area of the oatmeal container is 106.4 $in^{2}$.