Surface Area & Volume of Spheres Section 11-6. Vocab Sphere - the set of all points in space equidistant from a given point called the center. Radius.

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11.6 Surface Area and Volumes of Spheres

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Presentation transcript:

Surface Area & Volume of Spheres Section 11-6

Vocab Sphere - the set of all points in space equidistant from a given point called the center. Radius - segment that has one endpoint at the center and the other endpoint on the sphere. Diameter - segment passing through the center with endpoints on the sphere.

Surface Area of a Sphere

= 324Simplify. Find the surface area of the sphere below. Leave your answer in terms of. S.A. = 4 r 2 Use the formula for the surface area of a sphere. = Substitute r = = The surface area of the sphere is 324 ft 2.

Your turn Find the S.A. of a sphere with a diameter of 14 in. Give your answer two ways, in terms of π and rounded to the nearest square inch. 196π in 2 ; 616 in 2

S.A. = 4 r 2 Use the formula for the surface area of a sphere. 13 = 2 rSubstitute 13 for C. C = 2 rUse the formula for circumference. Step 1: Use the circumference to find the radius in terms of. The circumference of a rubber ball is 13 cm. Calculate its surface area to the nearest whole number. = rSolve for r Step 2: Use the radius to find the surface area. = 4 ( ) 2 Substitute for r To the nearest whole number, the surface area of the rubber ball is 54 cm 2. = Simplify Use a calculator.

Your turn Find the S.A. of a melon with a circumference of 18 in. Round your answer to the nearest ten square inches. 100 in 2

Volume of a sphere

Find the volume of the sphere. Leave your answer in terms of. V = r 3 Use the formula for the volume of a sphere = 15 3 Substitute r = = = 4500Simplify. The volume of the sphere is 4500 cm 3.

Your turn Find the volume to the nearest cubic inch of a sphere with a diameter of 60 inches. 113,097 in 3

The volume of a sphere is 1 in. 3. Find its surface area to the nearest tenth. Step 1: Use the volume to find the radius r. V = r 3 Use the formula for the volume of a sphere = r 3 Substitute = r 3 Solve for r = r Find the cube root of each side r Use a calculator.

Step 2: Use the radius to find the surface area. S.A. = 4 r 2 Use the formula for the surface area of a sphere. 4 ( ) 2 Substitute Use a calculator. To the nearest tenth, the surface area of the sphere is 4.8 in. 2. (continued)

Your Turn The volume of a sphere is 4200 ft 3. Find S.A. to the nearest tenth ft 3