R32 Selected Answers and SolutionsSelected Answers and Solutions
S.A. = 2 w + 2 h + 2 wh
= 2 · x · x + 2 · x · x + 2 · x · x
= 2 x^2 + 2 x^2 + 2 x^2 Multiply first. Then add like terms.
= 6 x^2
The formula for the surface area of a cube is
S.A. = 6 x^2.- 4 ft by 7 ft by 6 ft; The dimensions of the dunk
tank are suffi cient for a person to fall in and get wet. - False; Sample answer: A rectangular prism with
a length of 9 units, a width of 7 units, and height of
13 units has a surface area of 2(9 × 13) + 2(9 × 7) +
2(13 × 7) or 542 square units. If you double the
length, the surface area is 2(18 × 13) + 2(18 × 7) +
2(13 × 7) or 902 square units. So, 2 × 542 is 1,084.
1,084 ≠ 902 25. Sample answer: Surface area
measures the area of the faces, and area is
measured in square units. 27. G 29. 1,413.7 in^3
Pages 589–591 Lesson 10-2C
11 S.A. =^2 πrh +^2 πr^2 Surface area of a cylinder
= 2 π(2)(5) + 2 π(2)^2
Replace r with 2 and h
with 5.
≈ 88.0 Simplify.
The surface area is about 88.0 mm^2.- about 471.2 m^2 5. 1,215.8 m^2 7. 272.0 mm^2
- 1,120.0 in^2 11. 61.3 cm^2 13. Sample answer:
2 · 3 · 42 + 2 · 3 · 4 · 4 or 192 m^2
1515 Find the surface area of the tube.
S.A. = 2 πrh + 2 πr^2 Surface area of a cylinder
= 2 π(2.5)(15) + 2 π(2.5)^2 Replace with 15.r with 2.5 and h^
= 274.9 Simplify.
Find the curved surface of the tube.
S.A. = 2 πrh Curved surface of a cylinder
= 2 π(2.5)(15) Replace r with 2.5 and h with 15.
= 235.6 Simplify.
Find the percent of the tube that is cardboard.
235.6 = N · 274.9 Percent Equation
235.6_
274.9^ =^
N_ · 274.9
274.9^ Divide each side by 274.9.
0.857 = N Simplify.
Changing the decimal to a percent, about 85.7% of
the mail tube is cardboard.- Sample answer: Yes, it could make a difference.
As a rule, calculating with more decimal places
produces an answer closer to the exact value. - D 21. 23.08 ft^2 23. 3.5 in^3 25. 560 m^3
- 158.4 m^3
Pages 596–597 Lesson 10-2E
11 S.A. = B +^
_^1
2 P^ Surface area of a pyramid
= 25 + _ 21 (20 · 7) B =^5 · 5 or 25,
P = 4(5) or 20, = 7
= 95 Simplify.
The surface area of the pyramid is 95 in^2.- 3,829.5 ft^2 5. 507.5 mm^2 7. 2,079 cm^2 9. 26.1 ft^2
1111 S.A. = B +^ _^12 P^ Surface area of a pyramid
= 24 + _^12 (18 · 6) BP = = 6(3) or 20, 24, = 6
= 77 Simplify.
The surface area of the birdhouse is 77 in^2.- It would be shorter to climb up the slant height.
Sample answer: The bottom of the slant height is
closer to the center of the base of the pyramid. The
bottom of the lateral edge is farther from the center
of the base of the pyramid. 15. The formula is
based on fi nding the area of each base and then
adding them together. 17. H 19. 13,890 cm^2 - 301.6 ft^3
Pages 602–603 Lesson 10-3A PSI- Sample answer: Finding the areas of the separate
geometric fi gures and then adding is easier than
trying to fi nd the area of the irregular fi gure as a
whole. 3. 114 ft^2 5. 2 h
77 First fi nd the number of minutes in _^13 hour.
One third of 60 is 20. Make a chart.
Monday 45 45 min
Tuesday 45 + 20 65 min or 1 hr 5 min
Wednesday 1 hr 5 min + 20 min 1 hr 25 min
Thursday 1 hr 25 min + 20 min 1 hr 45 min
Friday 1 hr 45 min + 20 min 1 hr 65 min or 2 hr 5 min
Saturday 2 hr 5 min + 20 min 2 hr 25 min
Sunday 2 hr 25 min + 20 min 2 hr 45 min
2 hours 25 minutes - 76 students
Pages 608–610 Lesson 10-3C- 897 in^3 3. 870 cm^2 5. 39.6 in^2
77 The solid is composed of a rectangular prism
and a triangular prism. Let B 1 be the area of the
base of the rectangular prism, 1.8 · 1.1 or 1.98. Let
B 2 be the area of the base of the triangular prism,
(^1) _
2 · 1.8 · 0.7 or 0.63.
V = B 1 h 1 + B 2 h 2 Volume of rectangular prismvolume of triangular prism. +
= 1.98(0.8) + 0.63(1.1) Replace0.63, h B^1 with 1.98, B^2 with
1 with 0.8, h 2 with 1.1.
= 1.584 + 0.693
= 2.3 Simplify.
The volume of the solid, to the nearest tenth, is
2.3 cubic meters.
- 1,476.5 m^2 11. 308.4 m^2 13. 718.9 in^2
1515 The solid is composed of a rectangular prism
and a triangular prism. Convert inches to feet
before calculating.
Find the volume of the rectangular prism.
R01_R42_EM_SelAns_895130.indd R32 1/18/10 9:51 AM