 EXAMPLE 3 Use the circumference of a sphere EXTREME SPORTS

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EXAMPLE 3 Use the circumference of a sphere EXTREME SPORTS In a sport called sphereing, a person rolls down a hill inside an inflatable ball surrounded by another ball. The diameter of the outer ball is 12 feet. Find the surface area of the outer ball. SOLUTION The diameter of the outer sphere is 12 feet, so the radius is = 6 feet. 12 2

EXAMPLE 3 Use the circumference of a sphere Use the formula for the surface area of a sphere. S = 4πr2 = 4π(62) = 144π The surface area of the outer ball is 144π, or about square feet. ANSWER

The circumference of the inner is 6π feet, so the radius is
GUIDED PRACTICE for Example 3 3. In Example 3, the circumference of the inner ball is 6π feet. Find the surface area of the inner ball. round your answer to two decimal places. SOLUTION The circumference of the inner is 6π feet, so the radius is 2πr = 6π Write formula for circumference of circle r = 3 Simplify S = 4πr2 Formula for surface area of a sphere = 4π 32 Substitute 3 for r = Use a calculator

GUIDED PRACTICE for Example 3 The surface area of the inner ball is about ft2 ANSWER

Find the volume of a sphere
EXAMPLE 4 Find the volume of a sphere The soccer ball has a diameter of 9 inches. Find its volume. SOLUTION The diameter of the ball is 9 inches, so the radius is = 4.5 inches. 9 2 V = πr3 4 3 Formula for volume of a sphere = π(4.5)3 4 3 Substitute.

Find the volume of a sphere
EXAMPLE 4 Find the volume of a sphere = 121.5π Simplify. Use a calculator. The volume of the soccer ball is 121.5π, or about cubic inches. ANSWER

Find the volume of a composite solid
EXAMPLE 5 Find the volume of a composite solid Find the volume of the composite solid. SOLUTION = πr2h – ( πr3) 1 2 4 3 Formulas for volume = π(2)2(2) – π(2)3 2 3 Substitute. 2 3 = 8π – (8π) Multiply.

Find the volume of a composite solid
EXAMPLE 5 Find the volume of a composite solid = π – π 24 3 16 Rewrite fractions using least common denominator. 8 3 = π Simplify. The volume of the solid is π, or about 8.38 cubic inches. 8 3 ANSWER

4. The radius of a sphere is 5 yards. Find the volume
GUIDED PRACTICE for Examples 4 and 5 4. The radius of a sphere is 5 yards. Find the volume of the sphere. Round your answer to two decimal places. SOLUTION v = πr3 4 3 Formula for volume of a sphere = π(5)3 4 3 Substitute. = Use a calculator The volume of the sphere is yd2 ANSWER

GUIDED PRACTICE for Examples 4 and 5
5. A solid consists of a hemisphere of radius 1 meter on top of a cone with the same radius and height 5 meters. Find the volume of the solid. Round your answer to two decimal places. SOLUTION Volume of solid Volume of hemisphere Volume of cone = + ( πr3) 1 2 4 3 + (πr2)h = Formulas for volume = 1 2 4 3 ( π13) + (π 12) 5 Substitute.

The volume of the solid is 7.33m2 ANSWER
GUIDED PRACTICE for Examples 4 and 5 = 7.33 Simplify The volume of the solid is 7.33m2 ANSWER

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