Question

On the way home from rug shopping, Sophia stopped and bought a rectangular cake. The bottom is not frosted, but all other sides are. The cake is 8 x 11 x 2 inches. Sophia also bought a cylinder shaped pineapple upside down cake. Only the top of the cake is covered in pineapples and icing. The area that is covered is 63.585 square inches.

A) What is the surface area of the rectangular cake that has frosting on it?


B) What is the radius of the pineapple cake?


C) What is the diameter of the pineapple cake?



please help! my brain isn't working properly today.

Answer 1

A) Total Surface Area = 164 sq. feet.

B) Radius = 4.5 inches

C) Diameter = 9 inches

Explanation:

A)

A rectangular prism has 6 faces. Since bottom is not covered in frosting, we only need to find area of all the 5 faces (surfaces) and sum it.

The length is 8, width is 11, and height is 2 (of the cake).

Hence, top surface is 8 * 11 = 88

There are 2 sides measuring 8 and 2. So area is 8*2= 16 *2 = 32

THere are other 2 sides measuring 11 and 2. So area is 11 * 2 = 22 * 2 = 44

Total surface area of the cake that has frosting = 88 + 32 + 44 = 164 sq. inches

B)

Top of the cylinder (pineapple cake) is covered in icing. Top is the shape of a circle, which has area
`\pi r^2`, which is given as 63.585

Solving for radius (r), we get:

`\pi r^2=63.585\\r^2=(63.585)/(\pi)\\r=\sqrt{(63.585)/(\pi)}\\ r=4.5`

radius = 4.5 inches

C)

The diameter is twice the length of the radius.

The diameter is thus D = 2 * r

D = 2 * 4.5 = 9

Diameter = 9 inches