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Sphereing: Surface Area and Volume Calculation for Inflatable Ball Sports

Calculate the surface area and volume of inflatable balls used in the extreme sport of Sphereing. Learn how to use the formulas and solve examples and guided practice exercises. Measurements are given in feet and inches.

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Sphereing: Surface Area and Volume Calculation for Inflatable Ball Sports

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  1. 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 12feet. Find the surface area of the outer ball. The diameter of the outer sphere is 12feet, so the 12 radius is = 6feet. 2 EXAMPLE 3 Use the circumference of a sphere EXTREME SPORTS SOLUTION

  2. ANSWER The surface area of the outer ball is 144π, or about 452.39 square feet. EXAMPLE 3 Use the circumference of a sphere Use the formula for the surface area of a sphere. S = 4πr2 = 4π(62) = 144π

  3. for Example 3 GUIDED PRACTICE 3. In Example 3, the circumference of the inner ball is 6πfeet. Find the surface area of the inner ball. round your answer to two decimal places. SOLUTION The circumference of the inner is 6πfeet, 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 = 113.13 Use a calculator

  4. ANSWER The surface area of the inner ball is about113.13ft2 for Example 3 GUIDED PRACTICE

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

  6. ANSWER The volume of the soccer ball is 121.5π, or about 381.70 cubic inches. Find the volume of a sphere EXAMPLE 4 = 121.5π Simplify. ≈ 381.70 Use a calculator.

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

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

  9. 4 v = πr3 3 4 = π(5)3 ANSWER 3 The volume of the sphere is 523.81yd2 for Examples 4 and 5 GUIDED PRACTICE 4. The radius of a sphere is 5 yards. Find the volume of the sphere. Round your answer to two decimal places. SOLUTION Formula for volume of a sphere Substitute. = 523.81 Use a calculator

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

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

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