SOLUTION: A circular piece of paper has a 5 cm radius. It is cut once through to the center and curled up to form a model of a cone with a height of 4 cm. Find the volume and surface area of

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A circular piece of paper has a 5 cm radius. It is cut once through to the center and curled up to form a model of a cone with a height of 4 cm. Find the volume and surface area of      Log On

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Question 258341: A circular piece of paper has a 5 cm radius. It is cut once through to the center and curled up to form a model of a cone with a height of 4 cm. Find the volume and surface area of the cone.

Answer by Theo(13342) About Me  (Show Source):
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the length of the side of this cone will be 5 cm.

the length of the altitude of this cone will be 4 cm.

this should form a 3/4/5 right triangle.

this makes the radius of the base of the cone equal to 3 cm.

volume of the cone is equal to 1/3 * pi * r^2 * h.

this becomes 1/3 * pi * 9 * 4 = 1/3 * pi * 36 = 12 * pi cubic cm.

surface area of the cone is equal to pi * r * (r + s).

this becomes pi * 3 * (3 + 5) = pi * 3 * 8 = 24 * pi square cm.