Chapter 12 - Surface Area & Volume of Solids

Objectives:

Identify types of solidsCalculate surface area & volume of: Prisms Pyramids Cylinders Cones Spheres

12.6 Surface Area & Volume of Spheres

Objectives:Find the volume of a sphereFind the surface area of a sphere

What is a sphere?

A sphere is the locus of points in space that are a given distance from a point.

That 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.

Surface Area of a Sphere

S = 4πr2

More Sphere Terms

If a plane intersects a sphere, the intersection is . . .

either a single point or a plane If the plane contains the center of the sphere,

then the intersection is a great circle of the sphere.

Every great circle of a sphere separates the sphere into 2 congruent halves called hemispheres.

Example

A baseball has a radius of 1.45 inches. How much leather does it take to cover

the baseball?S = 4πr2

S = 4π*1.45*1.45S = 26.4 “2

Volume of a Sphere

V = 4/3 πr3

Example

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.

h = 2 cm

r = 1 cm

Example

Find the volume of the cylinder:V = πr2h = π*1*1*2 = 2πFind the radius of the sphere:V = 4/3 πr3

2π = 4/3 πr3 (multiply both sides by 3)

6π = 4πr3 (Divide each side by 4π)

1.5 = r3 (take cube root with a calculator)

r = 1.14

h = 2 cm

r = 1 cm

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Study for tomorrow’s test!