Question

OK, I cut a cake vertically to make 2 congruent parts. a) Find the perimeter and area of the cross section formed by the cut. Write your answer as a decimal. The perimeter is __ inches and the area is __ square inches. b) Find the surface area of the cake that is not frosted before the cut. Round your answer to the nearest hundredth. The surface area is about __square inches.

Answer 1

The perimeter is 36.5 inches.

The area is 59.5 square inches.

The surface area is about 153.94 square inches.

Explanation:

From the figure it is clear that,

Radius of cake = 7 in

Diameter of cake = 14 in

Height = 4.25 in

We need cut the cake vertically along its diameter to make 2 congruent parts.

So, cross section is a rectangle of length 4.25 in and width 14 in.

Perimeter of rectangle is

`Perimeter=2(length+width)`

`Perimeter=2(4.25+14)`

`Perimeter=2(18.25)`

`Perimeter=36.5`

The perimeter is 36.5 inches.

Area of rectangle is

`Area=lengt* width`

`Area=4.25* 14`

`Area=59.5`

The area is 59.5 square inches.

We need to find the surface area of the cake that is not frosted before the cut. It means the area of base.

Area of circle =
`\pi r^2`

where, r is radius.

Area of circular base =
`\pi (7)^2`

`=49\pi`

`=153.93804`

`\approx 153.94`

Therefore, the surface area is about 153.94 square inches.