Glencoe Math: Course 3, Volume 2
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Glencoe Math: Course 3, Volume 2 View details
6. Changes in Dimensions
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Exercise 29 Page 648

Use the formulas for the surface area of a cone.

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The given solid is a cone with a diameter of centimeters and a height of centimeters.

To calculate the surface area of a cone, we can use the known formula where is the radius of the base and is the slant height of the cone.
Looking at the diagram, we know that the diameter of the cone's base is centimeters. By dividing by we get the radius of the base.
We now know that the radius of the cone is centimeters and that the height of the cone is centimeters. Now, we can focus on the right triangle created within the cone.
The slant height of the cone is the hypotenuse of the triangle. The legs of the triangle are the height of the pyramid and the radius of the base. Notice that we can find the slant height of the cone using the Pythagorean Theorem.
Let's substitute for and for into the above equation to find the slant height of the cone.
Solve for
We found that the slant height is about centimeters. Note that, when solving the above equation, we only kept the principal root because represents a side length and must be a positive number. Let's now substitute with and with into the formula, we can calculate
Simplify right-hand side
The surface area of the cone is approximately square centimeters.