Find the surface area of a sphere

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Presentation transcript:

Find the surface area of a sphere EXAMPLE 1 Find the surface area of a sphere Find the surface area of the sphere. SOLUTION S = 4πr2 Formula for surface area of a sphere. = 4π(82) Substitute 8 for r. = 256π Simplify. ≈ 804.25 Use a calculator. The surface area of the sphere is about 804.25 square inches. ANSWER

Standardized Test Practice EXAMPLE 2 Standardized Test Practice SOLUTION S = 4πr2 Formula for surface area of a sphere. 20.25π = 4πr2 Substitute 20.25π for S. 5.0625 = r2 Divide each side by 4π. 2.25 = r Find the positive square root.

EXAMPLE 2 Standardized Test Practice The diameter of the sphere is 2r = 2 2.25 = 4.5 centimeters. The correct answer is B. ANSWER

GUIDED PRACTICE for Examples 1 and 2 2. The surface area of a sphere is 30π square meters. Find the radius of the sphere. about 2.74 meters ANSWER

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 circumference of the outer ball is 12π feet. Find the surface area of the outer ball. SOLUTION The circumference of the outer sphere is 12π feet, so the radius is = 6 feet. 12π 2π

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 452.39 square feet. ANSWER

Find the volume of a sphere EXAMPLE 4 Find the volume of a sphere A 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. ≈ 381.70 Use a calculator. The volume of the soccer ball is 121.5π, or about 381.70 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