Holt Geometry

10-8 Spheres

Warm UpFind each measurement.

1. the radius of circle M if the diameter is 25 cm

2. the circumference of circle X if the radius is

42.5 in.

3. the area of circle T if the diameter is 26 ft

4. the circumference of circle N if the area is

625 cm2

12.5 cm

85 in.

169 ft2

50 cm

Holt Geometry

10-8 Spheres

10-8 Spheres

Holt Geometry

Holt Geometry

10-8 Spheres

A sphere is the locus of points in space that are a fixed distance from a given point called the center of a sphere. A radius of a sphere connects the center of the sphere to any point on the sphere. A hemisphere is half of a sphere. A great circle divides a sphere into two hemispheres

Holt Geometry

10-8 Spheres

Holt Geometry

10-8 Spheres

Example 1A: Finding Volumes of Spheres

Find the volume of the sphere. Give your answer in terms of .

= 2304 in3 Simplify.

Volume of a sphere.

Holt Geometry

10-8 Spheres

Example 1B: Finding Volumes of Spheres

Find the diameter of a sphere with volume 36,000 cm3.

Substitute 36,000 for V.

27,000 = r3

r = 30

d = 60 cm d = 2r

Take the cube root of both sides.

Volume of a sphere.

Holt Geometry

10-8 Spheres

Example 2: Sports Application

A sporting goods store sells exercise balls in two sizes, standard (22-in. diameter) and jumbo (34-in. diameter). How many times as great is the volume of a jumbo ball as the volume of a standard ball?

standard ball: jumbo ball:

A jumbo ball is about 3.7 times as great in volume as a standard ball.

Holt Geometry

10-8 Spheres

Holt Geometry

10-8 Spheres

Example 3A: Finding Surface Area of Spheres

Find the surface area of a sphere with diameter 76 cm. Give your answers in terms of .

S = 4r2

S = 4(38)2 = 5776 cm2

Surface area of a sphere

Holt Geometry

10-8 Spheres

Example 3C: Finding Surface Area of Spheres

Find the surface area of a sphere with a great circle that has an area of 49 mi2.

Substitute 49 for A.49 = r2

r = 7 Solve for r.

S = 4r2

= 4(7)2 = 196 mi2 Substitute 7 for r.

A = r2 Area of a circle

Holt Geometry

10-8 Spheres

Example 5: Finding Surface Areas and Volumes of Composite Figures

Find the surface area and volume of the composite figure. Give your answer in terms of .

Step 1 Find the surface area of the composite figure.

The surface area of the composite figure is the sum of the curved surface area of the hemisphere, the lateral area of the cylinder, and the base area of the cylinder.

Holt Geometry

10-8 Spheres

Check It Out! Example 5

Find the surface area and volume of the composite figure.

Step 1 Find the surface area of the composite figure.

The surface area of the composite figure is the sum of the curved surface area of the hemisphere, the lateral area of the cylinder, and the base area of the cylinder.

Holt Geometry

10-8 Spheres

Lesson Quiz: Part I

Find each measurement. Give your answers in terms of .

1. the volume and surface areaof the sphere

2. the volume and surface area of a sphere with great circle area 36 in2

3. the volume and surface areaof the hemisphere

V = 36 cm3; S = 36 cm2

V = 288 in3;S = 144 in2

V = 23,958 ft3;S = 3267 ft2

Holt Geometry

10-8 Spheres

Lesson Quiz: Part II

4. A sphere has radius 4. If the radius is multiplied

by 5, describe what happens to the surface area.

5. Find the volume and surface area of the

composite figure. Give your answer in terms of .

The surface area is multiplied by 25.

V = 522 ft3; S = 267 ft2