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 L of a right circular cone is L=π r l, where r is the radius of the base and l is the slant height.
We know from the graph that the radius of the base is equal to 2.5 centimeters. To find the lateral area, we need to also know the cone's slant height l. We can do that using the Pythagorean Theorem.
We can see that there is a right triangle with leg lengths of 2.5 and 9 centimeters. Also, the length of the hypotenuse is equal to l. Let's substitute these values into the Pythagorean Theorem.
Since l is a measure, it must be a positive value. Therefore, we found that the slant height of the cone l is equal to 9.34 centimeters. Now, we can substitute r=2.5 and l=9.34 into the equation of the lateral area L of the cone.
We found that the lateral area of the cone, which is also the amount of paper needed to make the drinking cup, is about 73.4 centimeters squared. This result corresponds with option F.
