Selected Answers and Solutions R31Selected Answers and Solutions
For Homework Help, go to Hotmath.comair condition the space is 9,600 ft^3 · $0.11/ft^3 or
$1,056 per year. To find the average cost per
month, divide the yearly cost by 12. On average,
it costs $1,056 ÷ 12 or $88 to air condition the
office for one month.
23a. Sample answer: There is a direct relationship
between the volume and the length. Since the
length is doubled, the volume is also doubled.
23b. The volume is eight times greater.
23c. neither; Sample answer: Doubling the height
will result in a volume of 4 · 4 · 10 or 160 in^3 ;
doubling the width will result in a volume of
4 · 8 · 5 or 160 in^3. 25. Sample answer: They are
similar in that the volume is the product of the area
of the base and the height of the prism. They are
different in the formulas used to fi nd the area of
the base of the fi gure. 27. 864 29. BPages 565–568 Lesson 10-1C- 141.4 in^3
33 V = πr^2 h^ Volume of a cylinder
V = π(5.5)^2 6.5 Replace r with 5.5 and h with 6.5.
V = 617.7 ft^3 Simplify. - 603.2 cm^3 7. 4,071.5 ft^3 9. 2,770.9 yd^3 11. 35.6 m^3
(^1313) r = 1
2 d^
Relationship between diameter
and radius
r = 1 2 (4.5) or 2.25 Use d = 4.5. Simplify.
V = πr^2 h Volume of a cylinder
V = π(2.25)^2 6.5 Replace r with 2.25 and h with 6.5.
V = 103.4 Simplify.
The volume of the cylinder is about 103.4 m^3.
- 288.6 in^3 17. 34.4 in^3 19. 124,642.7 m^3 21. d
- a 25. 2,375 cm^3
2727 Let VA be the volume of cylinder A, and VB be
the volume of cylinder B.
VA = VB Both cylinders have the same volume.
πr^2 h = πr^2 h Volume of a cylinder
π(4)^22 = π(2)^2 h (^) For Cylinder For Cylinder AB, , rr = = 4 and 2. h = 2.
32 π = 4 πh Simplify.
32 4 ππ = ^44 ππh Divide each side by 4π.
8 = h Simplify.
The height of Cylinder B is 8 inches.
- Sample answer: The shorter cylinder, because
the radius is larger and that is the squared value in
the formula. 31. 1 to 2 33. Sample answer: In
both, the volume equals the area of the base times
the height. 35. 9 37. 75.36 cc^3
Pages 573–574 Lesson 10-1E
11 V =^1 _ 3 Bh^ Volume of a pyramidV = 1 3 ( 21 · 8 · (^6) ) 10 B = _ 21 · 8 · 6, h = 10
V = 80 Simplify.
The volume of the pyramid is 80 ft^3.
- 12 cm 5. 5,971,000 ft^3 7. 109.3 m^3 9. 14 in.
- 11 ft
1313 V =^1 3 Bh^ Volume of a pyramid
V = 1 3 (3 · 2.5)4 B = 3 · 2.5, h = 4
V = 10 Simplify.
The volume of glass used to create the pyramid
was 10 in^3. - Sample answer: fi rst set: area of the base, 40 ft^2 ;
height of the pyramid, 12 ft; second set: area of the
base, 30 ft^2 ; height of the pyramid, 16 ft. 19. The
volumes are the same. 21. B 23. 624.9 m^3 - 13,965 in^3
Pages 576–579 Lesson 10-1F- 2,668.3 m^3
33 V = 1 3 πr^2 h Volume of a pyramid
V = 1 3 π(1.75)^2 8.4 r =^1 _ 2 · 3.5 or 1.75, h = 8.4
V = 26.9 Simplify.
The volume of the pyramid is 26.9 ft^3. - 1.8 c 7. 4,720.8 mm^3 9. 2,989.8 mm^3
- 402.1 cm^3 13. about 7 c 15. 10 mm
1717 Let h be the height of the cylinder, H be the
height of the cone, and r be the radius of both.
πr^2 h = ^13 πr^2 H The volume of the cylinder is equal to the volume of the cone.
π(5)^2 (12) = 31 π(5)^2 H r = 5, h = 12
300 π = 31 (25)πH Simplify.
900 π = 25 πH Multiply both sides by 3.
^90025 ππ = _^2525 ππH Divide each side by 25π.
36 = H Simplify.
The height of the cylinder is 36 cm. - 4.5 m 21. 3.0 yd 23. Aisha used the incorrect
radius; 25.1 in^3 25. Sample answer: Depending on
the length of the radius and the height, generally
doubling the radius has more effect as it is squared
in the formula. 27. A 29. 3.5 in^3 31. 129.5 m^3
Pages 585–587 Lesson 10-2B- 108 ft^2 3. Yes; the surface area of the box is
252 in^2. The surface area of the paper is 288 in^2.
Since 252 in^2 < 288 in^2 , she has enough paper. - 314 cm^2
77 Replace with 12.3, w with 8.5, and h with 15.
S.A. = 2 w + 2 h + 2 wh
= 2 · 12.3 · 8.5 + 2 · 12.3 · 15 + 2 · 8.5 · 15
= 209.1 + 369 + 255 Multiply first. Then add.
= 833.1
The surface area of the prism is 833.1 mm^2. - 125.4 in^2 11. 207 in^2 13. 1,128.8 m^2
- 192 cm^2 17. 64.5 in^2
1919 Remember that each edge of a cube has the
same measure. Replace with x, w with x, and h
with x.
R01_R42_EM_SelAns_895130.indd R31 1/18/10 9:51 AM