ACT Math : How to find the surface area of a cone

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #141 : Solid Geometry

Some conical party hats are being decorated with glitter paper. If the base of the hats is  inches across and the slant height is  inches, how many square inches of glitter paper are needed to decorate one hat?

Possible Answers:

Correct answer:

Explanation:

The formula for the surface area of a cone is

, where  is the slant height. Since we're only concerned with the slant height portion of the surface area formula, we can ignore the  portion of the equation.

Plug in known values to this part of the equation and solve.

So, each hat requires  of glitter paper.

Example Question #142 : Solid Geometry

The surface area of a cone equals If the radius of the cone equals , what is the height of the cone?

Possible Answers:

Correct answer:

Explanation:

To solve this question, you need to know the surface area of a cone equation:   where  is the radius of the cone , and  is the height of the cone.  We must substitute all of the values that we know, and solve for the height of the cone to get the answer.   

  Therefore, the height of the cone is 

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