Evelyn’s made a cake in the shape of a circus tent to use as the centerpiece at the celebration. As shown in the illustration, the cake consisted of a cylinder and a cone. The height of the cone is half the height of the cylinder. The volume of the cylinder is 1470 in3. The diameter of the cylinder is 12 in. What is the volume of the circus tent cake? Use 3.14 for π. Round to the nearest hundredth. Show your work.
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Question

Evelyn’s made a cake in the shape of a circus tent to use as the centerpiece at the celebration. As shown in the illustration, the cake consisted of a cylinder and a cone. The height of the cone is half the height of the cylinder. The volume of the cylinder is 1470 in3. The diameter of the cylinder is 12 in. What is the volume of the circus tent cake? Use 3.14 for π. Round to the nearest hundredth. Show your work. 
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gokuporter · Answer

@Directrix I have the illustration. :)

gokuporter · Answer

@Directrix are you there?

directrix · Answer

I thought I tagged you about this problem last night.

directrix · Answer

The tag was to the discussion of this problem at the link: http://openstudy.com/study#/updates/5507823ae4b05989c3e023fb

gokuporter · Answer

Yes

gokuporter · Answer

Can you explain step by step? I don't understand the formula.

directrix · Answer

Start with the cylinder:

The volume of the cylinder is 1470 in3. The diameter of the cylinder is 12 in

V of Cyl = B*h where B is the area of the base of the cylinder.

1470 = 3.14 * 6^2 * h

Solve that ^^^ for h.

gokuporter · Answer

1470 = 113.04 * h

directrix · Answer

What is 1470 divided by 113.04 =

directrix · Answer

@Gokuporter

gokuporter · Answer

13?

directrix · Answer

I got 13.0042. I guess I'll call it 13.

Now, get the volume of the cone.

Its height is  half that of the cylinder.

1/2  * 13 = 6.5

directrix · Answer

Volume of Cone = 1/3  *  3.14 * 6^2  * 6.5

Volume of Cone = ?

directrix · Answer

You can put this in the Google search box and the calculator will pop up with the result:

 1/3 * 3.14 * 6^2 * 6.5=

gokuporter · Answer

Volume of the Cone is 244.92

directrix · Answer

Volume of the Cone is 244.92 cubic inches

Volume of the Cylinder is 1470 cubic inches

Volume of entire cake is 244.92 + 1470 = ?

@Gokuporter

gokuporter · Answer

Volume of entire cake 244.92 + 1470 = 1714.92

directrix · Answer

cubic inches, yes. 

That is what I got.

gokuporter · Answer

@Directrix Thank you for the in-depth explaination. I will use this information for future problems. ^w^

directrix · Answer

You are welcome.

gokuporter · Answer

@Directrix We need to round to the nearest hundredth.

directrix · Answer

This is the nearest hundredth:   1714.92

Remember, we used 3.14 for pi which kept our calculations in the hundredths.

@Gokuporter