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Warm-Up Exercises
1. Right rectangular prism, side lengths 8 in., 5 in.,and 10 in.
2. Right cone, radius 3 m, height 4 m
ANSWER 340 in.2; 400 in.3
ANSWER 75.40 m2; 37.70 m3
Find the surface area and volume of each solid.
Warm-Up Exercises
3. Sphere, radius 7.3 ft
ANSWER 669.66 ft2; 1629.51 ft3
Find the surface area and volume of each solid.
Warm-Up ExercisesEXAMPLE 1 Identify similar solids
Tell whether the given right rectangular prism is similar to the right rectangular prism shown at the right.
a.b.
Warm-Up ExercisesEXAMPLE 1 Identify similar solids
SOLUTION
The prisms are similar because the ratios of corresponding linear measures are all equal. The scale factor is 2:3.
ANSWER
The prisms are not similar because the ratios of corresponding linear measures are not all equal.
ANSWER
a. Lengths48 Widths
24 Heights
22
b. Lengths46
Widths23
Heights23
12
= 12
= 11
=
23=
Warm-Up ExercisesGUIDED PRACTICE for Example 1
Tell whether the pair of right solids is similar. Explain your reasoning.
1.
The solids are similar because the ratios of corresponding sides is in the ratio 4:3
ANSWER
Warm-Up ExercisesGUIDED PRACTICE for Example 1
Tell whether the pair of right solids is similar. Explain your reasoning.
2.
The solids are similar because the ratios of corresponding sides is in the ratio 4:3
ANSWER
Warm-Up ExercisesEXAMPLE 2 Use the scale factor of similar solids
Packaging
The cans shown are similar with a scale factor of 87:100. Find the surface area and volume of the larger can.
Warm-Up ExercisesEXAMPLE 2
Volume of II ≈ 42.93
Surface area of II ≈ 68.49
The surface area of the larger can is about 68.49 square inches, and the volume of the larger can is about 42.93 cubic inches.
ANSWER
Use the scale factor of similar solids
Warm-Up ExercisesEXAMPLE 2
SOLUTION
Use Theorem 12.13 to write and solve two proportions.
Surface area of I
Surface area of II
51.84Surface area of II
Volume of I
Volume of II
28.27Volume of II
a2
b2=
=a3
b3
=872
1002
=873
1003
Use the scale factor of similar solids
Warm-Up ExercisesEXAMPLE 3 Find the scale factor
The pyramids are similar. Pyramid P has a volume of 1000 cubic inches and Pyramid Q has a volume of 216 cubic inches. Find the scale factor of Pyramid P to Pyramid Q.
Warm-Up ExercisesEXAMPLE 3 Find the scale factor
SOLUTION
Use Theorem 12.13 to find the ratio of the two volumes.a3
b3 = 1000216
The scale factor of Pyramid P to Pyramid Q is 5:3.
ANSWER
Write ratio of volumes.
Find cube roots.
Simplify.
ab = 6
10
ab =
53
Warm-Up ExercisesEXAMPLE 4 Checking Solutions of a Linear Inequality
A store sells balls of yarn in two different sizes. The diameter of the larger ball is twice the diameter of the smaller ball. If the balls of yarn cost $7.50 and $1.50, respectively, which ball of yarn is the better buy?
Volume of large ball
Volume of small ball
Consumer Economics
STEP 1
Compute: the ratio of volumes using the diameters.
23
13= =81
, or 8 : 1
Warm-Up ExercisesEXAMPLE 4 Checking Solutions of a Linear Inequality
Price of large ball
Volume of small ball
Find: the ratio of costs.
= , or 5:151
STEP 2
= $ 1.50$ 7.50
Warm-Up ExercisesEXAMPLE 4 Checking Solutions of a Linear Inequality
Compare: the ratios in Steps 1 and 2.
STEP 3
If the ratios were the same, neither ball would be a better buy. Comparing the smaller ball to the larger one, the price increase is less than the volume increase. So, you get more yarn for your dollar if you buy the larger ball of yarn.
ANSWER
The larger ball of yarn is the better buy.
Warm-Up ExercisesGUIDED PRACTICE for Examples 2, 3, and 4
Cube C has a surface area of 54 square units and Cube D has a surface area of 150 square units. Find the scale factor of C to D. Find the edge length of C, and use the scale factor to find the volume of D.
3.
Volume of D = 125 square units
ANSWER
Warm-Up ExercisesGUIDED PRACTICE
WHAT IF? In Example 4, calculate a new price for the larger ball of yarn so that neither ball would be a better buy than the other.
4.
for Examples 2, 3, and 4
ANSWER $12.00
