McGraw Hill Glencoe Geometry, 2012
MH
McGraw Hill Glencoe Geometry, 2012 View details
Standardized Test Practice

Exercise 2 Page 972

Recall the formula for the lateral area of a right cone.

F

Practice makes perfect

We are asked find the amount of paper that is needed to make a drinking cup from the given diagram.

The cup is in the shape of a right circular cone. Therefore, the amount of paper needed to make the cup is equal to the lateral area of the cone. Let's recall the formula for the lateral area.

The lateral area of a right circular cone is where is the radius of the base and is the slant height.

We know from the graph that the radius of the base is equal to centimeters. To find the lateral area, we need to also know the cone's slant height We can do that using the Pythagorean Theorem.

We can see that there is a right triangle with leg lengths of and centimeters. Also, the length of the hypotenuse is equal to Let's substitute these values into the Pythagorean Theorem.
Solve for

Since is a measure, it must be a positive value. Therefore, we found that the slant height of the cone is equal to centimeters. Now, we can substitute and into the equation of the lateral area of the cone.
Evaluate
We found that the lateral area of the cone, which is also the amount of paper needed to make the drinking cup, is about centimeters squared. This result corresponds with option F.