10-7
Exercises
KEYWORD: MG7 10-7
KEYWORD: MG7 Parent
GUIDED PRACTICE
1. Vocabulary The altitude of a pyramid is ? to the base. (perpendicular, parallel,
−−−−
or oblique)
SEE EXAMPLE
1
p. 705
Find the volume of each pyramid. Round to the nearest tenth, if necessary.
2.
3.
ÎÊ
ÊV“
{ÊÊȖе
£Çʈ˜°
{ÊV“
Èʈ˜°
{ʈ˜°
4. a hexagonal pyramid with a base area of 25 ft 2 and a height of 9 ft
3 mm
SEE EXAMPLE
2
p. 706
SEE EXAMPLE
3
p. 707
5. Geology A crystal is cut into the shape formed by two square
pyramids joined at the base. Each pyramid has a base edge
length of 5.7 mm and a height of 3 mm. What is the volume
to the nearest cubic millimeter of the crystal?
5.7 mm
Find the volume of each cone. Give your answers both in terms
of π and rounded to the nearest tenth.
6.
7.
£{ÊV“
Îäʈ˜°
Ó{ʈ˜°
™ÊV“
8. a cone with radius 12 m and height 20 m
SEE EXAMPLE 4
p. 708
Describe the effect of each change on the volume of the given figure.
9. The dimensions are tripled.
ÎÊV“
1.
10. The dimensions are multiplied by _
2
£xÊvÌ
xÊV“
™ÊvÌ
™ÊvÌ
SEE EXAMPLE
p. 708
5
Find the volume of each composite figure. Round to the nearest tenth, if necessary.
12.
11.
{ʈ˜°
nʈ˜°
£nÊV“
Èʈ˜°
£ÓÊV“
£Óʈ˜°
£ÓÊV“
£ÓÊV“
10-7 Volume of Pyramids and Cones
709
PRACTICE AND PROBLEM SOLVING
Independent Practice
For
See
Exercises Example
13–15
16
17–19
20–21
22–23
Find the volume of each pyramid. Round to the nearest tenth, if necessary.
13.
14.
1
2
3
4
5
Extra Practice
Skills Practice p. S23
Application Practice p. S37
™Ê“
£äÊvÌ
£Óʓ
xʓ
ÈÊvÌ
£Îʓ
nÊvÌ
15. a regular square pyramid with base edge length 12 ft and slant height 10 ft
16. Carpentry A roof that encloses
an attic is a square pyramid with
a base edge length of 45 feet and
a height of 5 yards. What is the
volume of the attic in cubic feet?
In cubic yards?
xÊÞ`
{xÊvÌ
Find the volume of each cone. Give your answers both in terms of π and rounded
to the nearest tenth.
17.
18.
{ʈ˜°
Óʈ˜°
{£Ê“
™Ê“
19. a cone with base area 36π ft 2 and a height equal to twice the radius
Describe the effect of each change on the volume of the given figure.
1.
20. The dimensions are multiplied by _
21. The dimensions are multiplied by 6.
3
{ÊvÌ
ӣʈ˜°
£xʈ˜°
ÇÊvÌ
ÇÊvÌ
Find the volume of each composite figure. Round to the nearest tenth, if necessary.
22.
23.
ÈÊvÌ
ÎÊvÌ
£äÊvÌ
xÊvÌ
ÓÊvÌ
£äÊvÌ
Find the volume of each right cone with the given dimensions. Give your answers in
terms of π.
24. radius 3 in.
height 7 in.
710
Chapter 10 Spatial Reasoning
25. diameter 5 m
height 2 m
26. radius 28 ft
slant height 53 ft
27. diameter 24 cm
slant height 13 cm
10-8
Exercises
KEYWORD: MG7 10-8
KEYWORD: MG7 Parent
GUIDED PRACTICE
1. Vocabulary Describe the endpoints of a radius of a sphere.
SEE EXAMPLE
1
p. 714
Find each measurement. Give your answers in terms of π.
2. the volume of the hemisphere
3. the volume of the sphere
£Ê“
££Êˆ˜°
4. the radius of a sphere with volume 288π cm 3
SEE EXAMPLE
2
p. 715
5. Food Approximately how many times as great is the volume of the grapefruit
as the volume of the lime?
£äÊV“
SEE EXAMPLE
3
p. 716
xÊV“
Find each measurement. Give your answers in terms of π.
6. the surface area of the sphere
7. the surface area of the sphere
£ÈÊÞ`
ÊÊ{™ûV“ÊÓ
8. the volume of a sphere with surface area 6724π ft 2
SEE EXAMPLE 4
p. 716
Describe the effect of each change on the given measurement of the figure.
9. surface area
10. volume
1.
The dimensions are multiplied by _
4
The dimensions are doubled.
£xʈ˜°
SEE EXAMPLE
p. 717
5
£ÈÊV“
Find the surface area and volume of each composite figure.
11.
xÊvÌ
ÓÊvÌ
Óʈ˜°
12.
Îʈ˜°
718
Chapter 10 Spatial Reasoning
nʈ˜°
PRACTICE AND PROBLEM SOLVING
Independent Practice
For
See
Exercises Example
13–15
16
17–19
20–21
22–23
Find each measurement. Give your answers in terms of π.
13. the volume of the sphere
1
2
3
4
5
Extra Practice
Skills Practice p. S23
Application Practice p. S37
14. the volume of the hemisphere
£nÊV“
ÇÊvÌ
15. the diameter of a sphere with volume 7776π in
3
16. Jewelry The size of a cultured pearl is typically
indicated by its diameter in mm. How many times
as great is the volume of the 9 mm pearl as the
volume of the 6 mm pearl?
Èʓ“
™Ê““
Find each measurement. Give your answers in terms of π.
17. the surface area of the sphere
18. the surface area of the sphere
ӣʈ˜°
ÊÊn£ûˆ˜ÊÓ 19. the volume of a sphere with surface area 625π m 2
Describe the effect of each change on the given measurement of the figure.
20. surface area
1.
The dimensions are multiplied by _
5
21. volume
The dimensions are multiplied by 6.
£°ÓÊvÌ
£{ʓ“
Find the surface area and volume of each composite figure.
22.
23.
ÎÊV“
{ÊV“
xÊV“
£äʓ“
Ó{ʓ“
nʓ“
£äÊV“
24. Find the radius of a hemisphere with a volume of 144π cm 3.
25. Find the circumference of a sphere with a surface area of 60π in 2.
26. Find the volume of a sphere with a circumference of 36π ft.
27. Find the surface area and volume of a sphere centered at (0, 0, 0) that passes
through the point (2, 3, 6).
28. Estimation A bead is formed by drilling a cylindrical hole with
a 2 mm diameter through a sphere with an 8 mm diameter.
Estimate the surface area and volume of the bead.
10 - 8 Spheres
719