Question

Indra baked and frosted a rectangular cake to sell at a bake sale for the Model UN club. The cake, including frosting, was 4 inches high, 16 inches wide, and 12 inches long. She centered the cake on a circular tray. The circular tray had a radius of 10 inches. What is the area, to the nearest square inch, of the tray that is not covered by the cake?

A. 100
B. 114
C. 122
D. 314
E. 192

Answer 1

C. 122

Explanation:

Given,

Dimension of the cake:

Length = 12 in Width = 16 in Height = 4 in

We have to find out the area of the tray that is not covered by the cake.

Indra centered the cake on a circular tray.

Radius of the tray = 10 in.

So area of the tray is equal to π times square of the radius.

Framing in equation form, we get;

Area of tray =
`\pi* r^2=3.14*{10}^2=3.14* 100=314\ in^2`

Since the cake is placed in circular tray.

That means only base area of cake has covered the tray.

Base Area of cake =
`length* width=12* 16=192\ in^2`

Area of the tray that is not covered by the cake is calculated by subtracting area of base of cake from area of circular tray.

We can frame it in equation form as;

Area of the tray that is not covered by the cake = Area of tray - Base Area of cake

Area of the tray that is not covered by the cake =
`314-192=122\ in^2`

Hence The area of the tray that is not covered by the cake is 122 sq. in.