Section Volume of Spheres

Parts of a Sphere The point is called the center of the sphere. A radius of a sphere is a segment from the center to a point on the sphere. A chord of a sphere is a segment whose endpoints are on the sphere. A diameter is a chord that contains the center. As with all circles, the terms radius and diameter also represent distances, and the diameter is twice the radius.

The volume of a sphere with radius r is

Example 1 The figure represents a spherical helium-filled balloon. This tourist attraction allows up to 28 passengers at a time to ride in a gondola suspended underneath the balloon. How much helium, to the nearest hundred gallons, does the balloon hold? (Hint: 1 gal = ft 3 ). d = 60 feet

Example 2 A spherical water tank has a diameter of 34 meters. How much water can the tank hold, to the nearest liter? (Hint: 1,000 Liters = 1m 3 )

Example 3 Find the volume of the composite figure. Round to the nearest cubic centimeter.

Example 4: To make a steel ball bearing, a cylindrical slug is heated and pressed into a spherical shape with the same volume. Find the radius of the ball bearing to the right: To find the volume of the slug, use the formula for the volume of a cylinder. V =  r 2 h =  (1 2 )(2) = 2(3.14) = 6.28 cm 3 Next…To find the radius of the ball bearing, use the formula for the volume of a sphere and solve for r.

V =4/3  r = 4/3(3.14)r = 4(3.14)r = (12.56)r = r  r Formula for volume of a sphere. Substitute 6.28 for V. Multiply each side by 3. Divide each side by Use a calculator to take the cube root. So, the radius of the ball bearing is about 1.14 cm.

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