91Ó°ÊÓ

A frustum of a cone is the part of the cone that lies between the base and a plane parallel to the base, as shown. Write a formula for the volume of the frustum of a cone in terms of, b, and h. (Hint: Consider the "missing" top of the cone and use similar triangles.)

REASONING EF is an arc on a circle with radius \(\mathrm{r}\) . Let \(\mathrm{x}^{\circ}\) be the measure of EF Describe the effect on the length of EF if you (a) double the radius of the circle, and (b) double the measure of EF.

PROBLEM SOLVING Over 2000 years ago, the Greek scholar Eratosthenes estimated Earth's circumference by assuming that the Sun's rays were parallel. He chose a day when the Sun shone straight down into a well in the city of Syene. At noon, he measured the angle the Sun's rays made with a vertical stick in the city of Alexandria. Eratosthenes assumed that the distance from Syene to Alexandria was equal to about 575 miles. Explain how Eratosthenes was able to use this information to estimate Earth's circumference. Then estimate Earth's circumference.

In Exercises 29–34, tell whether it is possible for a cross section of a cube to have the given shape. If it is, describe or sketch how the plane could intersect the cube. rhombus

In Exercises 29–34, tell whether it is possible for a cross section of a cube to have the given shape. If it is, describe or sketch how the plane could intersect the cube. isosceles triangle

MODELING WITH MATHEMATICS The Great Blue Hole is a cylindrical trench located off the coast of Belize. It is approximately 1000 feet wide and 400 feet deep. About how many gallons of water does the Great Blue Hole contain? (1 \(\mathrm{ft}^{3} \approx 7.48\) gallons)

You friend claims that if the radius of a sphere is doubled, then the surface area of the sphere will also be doubled. Is your friend correct? Explain your reasoning.

USING STRUCTURE ind the circumference of each circle. a. a circle circumscribed about a right triangle whose legs are 12 inches and 16 inches long b. a circle circumscribed about a square with a side length of 6 centimeters c. a circle inscribed in an equilateral triangle with a side length of 9 inches

In Exercises 29–34, tell whether it is possible for a cross section of a cube to have the given shape. If it is, describe or sketch how the plane could intersect the cube. scalene triangle

A semicircle with a diameter of 18 inches is rotated about its diameter. Find the surface area and the volume of the solid formed.