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HELP VOLUMES

1. 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.



Answer :

iGreen
V = pi * r^2 * h

Plug in what we know:

1470 = 3.14 * 6^2 * h

Find the height:

Simplify exponent:

1470 = 3.14 * 36 * h

Multiply:

1470 = 113.04h

Divide 113.04 to both sides:

h = 13

The height of the cone is half the height of the cylinder.

Cylinder height = 13

Cone height = 13 / 2 = 6.5

Radius of the cone should be the same as the cylinder.

V = 1/3 * pi * r^2 * h

V = 1/3 * 3.14 * 6^2 * 6.5

Simplify exponent:

V = 1/3 * 3.14 * 36 * 6.5

Multiply:

V = 244.92

Add the two volumes:

1470 + 244.92 = 1714.92
Panoyin
V = πr²h
1,470 = (3.14)(6)²h
1,470 = (3.14)(36)h
1,470 = 113.04h
113.04   113.04
13.00425 ≈ h

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