Question

1. A cake in the shape of a circus tent is used as a centerpiece at a celebration. The cake consists of a cylinder and a cone. The cylinder has a diameter of 12 inches and a height of 14 inches. The cone has a height of 6 inches. What is the volume of the cake? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi. Show your work.
(Please show me how you get your answers)
I nEED HELP!

Answer 1

Let us divide the shape of the cake into two parts:

1) The cylindrical part.
2) The cone of the tent.

Note: In order to find the total volume of the cake, we have to add the volumes of both of the above-mentioned part.


1.
The volume of the cylinder = $\pi *r^{2}*h$ --- (A)

We have the height = h = 14 inches.
Radius = r = Diameter / 2 = 12/2 = 6 inches.

and $\pi$= 3.14

Put the above values in equation (A);
(A) => The volume of the cylinder = (3.14) * (6 x 6) * (14) = 1582.56 inches cubed

2. 
The volume of the cone = $\pi *r^{2}* \frac{h}{3}$ --- (B)

Since the cake is in "circus tent" shape, therefore, the radius of the cone should be equal to the radius of the cylinder.

Radius of the cone = r = 6 inches.
Height of the cone = h = 6 inches.

and $\pi$= 3.14

Put the above values in equation (B);
(B) => The volume of the cone = (3.14) * (6 x 6) * (6 / 3) = 226.08 inches cubed

The volume of the cake = Volume of the cylinder + Volume of the cone
$V_{cake}$  = 1582.56 + 226.08 = 1808.64 inches cubed

Ans: The volume of the cake = 1808.64 $in^{3}$

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