9.7: Exercise Supplement

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Measurement and the United States System

Exercise $\PageIndex{1}$

What is measurement?

Answer: Measurement is comparison to a standard (unit of measure).

For problems 2-6, make each conversion. Use the conversion table given in Section 7.1.

Exercise $\PageIndex{2}$

9 ft= yd

Exercise $\PageIndex{3}$

32 oz= lb

Answer: 2 pounds

Exercise $\PageIndex{4}$

1,500 mg = g

Exercise $\PageIndex{5}$

12,000 lb = T

Answer: 6 tons

Exercise $\PageIndex{6}$

5,280 ft= mi

For problems 7-23, make each conversion.

Exercise $\PageIndex{7}$

23 yd to ft

Answer: 69 feet

Exercise $\PageIndex{8}$

$2 \dfrac{1}{2}$ mi to yd

Exercise $\PageIndex{9}$

8 in. to ft

Answer: $\dfrac{2}{3} = 0.66\overline{6} \text{ feet}$

Exercise $\PageIndex{10}$

51 in. to mi

Exercise $\PageIndex{11}$

3 qt to pt

Answer: 6 pints

Exercise $\PageIndex{12}$

8 lb to oz

Exercise $\PageIndex{13}$

5 cups to tbsp

Answer: 80 tablespoons

Exercise $\PageIndex{14}$

9 da to hr

Exercise $\PageIndex{15}$

$3 \dfrac{1}{2}$ min to sec

Answer: 210 seconds

Exercise $\PageIndex{16}$

$\dfrac{3}{4}$ wk to min

The Metric System of Measurement

Exercise $\PageIndex{17}$

250 mL to L

Answer: $\dfrac{1}{4} = 0.25$ L

Exercise $\PageIndex{18}$

18.57 cm to m

Exercise $\PageIndex{19}$

0.01961 kg to mg

Answer: 19,610 mg

Exercise $\PageIndex{20}$

52,211 mg to kg

Exercise $\PageIndex{21}$

54.006 dag to g

Answer: 540.06 g

Exercise $\PageIndex{22}$

1.181 hg to mg

Exercise $\PageIndex{23}$

3.5 kL to mL

Answer: 3,500,000 mL

Simplification of Denominate Numbers

For problems 24-31, perform the indicated operations. Simplify, if possible.

Exercise $\PageIndex{24}$

Add 8 min 50 sec to 5 min 25 sec.

Exercise $\PageIndex{25}$

Add 3 wk 3 da to 2 wk 5 da

Answer: 6 weeks 1 day

Exercise $\PageIndex{26}$

Subtract 4 gal 3 qt from 5 gal 2 qt.

Exercise $\PageIndex{27}$

Subtract 2 gal 3 qt 1pt from 8 gal 2 qt.

Answer: 5 gallons 2 quarts 1 pint

Exercise $\PageIndex{28}$

Subtract 5 wk 4 da 21 hr from 12 wk 3 da 14 hr.

Exercise $\PageIndex{29}$

Subtract 2 T 1,850 lb from 10 T 1,700 lb.

Answer: 7 T 1,850 pounds

Exercise $\PageIndex{30}$

Subtract the sum of 2 wk 3 da 15 hr and 5 wk 2 da 9 hr from 10 wk.

Exercise $\PageIndex{31}$

Subtract the sum of 20 hr 15 min and 18 hr 18 min from the sum of 8 da 1 hr 16 min 5 sec.

Answer: 7 days, 11 hours, 56 minutes, 7 seconds

For problems 32-43, simplify, if necessary.

Exercise $\PageIndex{32}$

18 in.

Exercise $\PageIndex{33}$

4 ft

Answer: 1 yard 1 foot

Exercise $\PageIndex{34}$

23 da

Exercise $\PageIndex{35}$

3,100 lb

Answer: 1 ton 1,100 pounds

Exercise $\PageIndex{36}$

135 min

Exercise $\PageIndex{37}$

4 tsp

Answer: 1 tablespoon 1 teaspoon

Exercise $\PageIndex{38}$

10 fl oz

Exercise $\PageIndex{39}$

7 pt

Answer: 3 quarts 1 pint

Exercise $\PageIndex{40}$

9 qt

Exercise $\PageIndex{41}$

2,300 mm

Answer: 2.3 meters

Exercise $\PageIndex{42}$

14,780 mL

Exercise $\PageIndex{43}$

1,050 m

Answer: 1.05 km

Perimeter, Circumference, Area and Volume of Geometric Figures and Objects ([link],[link])

For problems 44-58, find the perimeter, circumference, area or volume.

Exercise $\PageIndex{44}$

Perimeter, area

$A rectangle. The rectangle's height is 20mm, and its width is 50mm.$

Exercise $\PageIndex{45}$

Approximate circumference

$A circle. The circle's diameter is 1.8cm.$

Answer: 5.652 sq cm

Exercise $\PageIndex{46}$

Approximate volume

$A cone. The cone's radius is 3in and the cone's height is 8in.$

Exercise $\PageIndex{47}$

Approximate volume

$A cylinder. The cylinder's radius is 3.8ft, and its height is 2.3ft.$

Answer: 104.28568 cu ft

Exercise $\PageIndex{48}$

Exact area

$A circle. The circle's diameter is 5m.$

Exercise $\PageIndex{49}$

Exact area

$A half-circle with radius 0.6in.$

Answer: 0.18ππ sq in.

Exercise $\PageIndex{50}$

Exact volume

$A cylinder with a half-sphere on top. The object's radius is 4.2cm, and the cylinder's height is 10.1cm.$

Exercise $\PageIndex{51}$

Approximate volume

$A sphere with radius 8mm.$

Answer: 267.94667 cu mm

Exercise $\PageIndex{52}$

Area

$A trapezoid with bottom base 5.1in, top base 4.1in, and height 3.9in.$

Exercise $\PageIndex{53}$

Volume

$A rectangular solid with width 8cm, length 2cm, and height 2cm.$

Answer: 32 cu cm

Exercise $\PageIndex{54}$

Exact area

$A complex shape involving two circles and a circular cutout.$

Exercise $\PageIndex{55}$

Approximate area

$A rectangle with a half-circle cut out of it. The rectangle's width, which is also the diameter of the half-circular cutout, is 12in. The rectangle's height is 8in.$

Answer: 39.48 sq in.

Exercise $\PageIndex{56}$

Exact area

$A shape composed of four circles overlapping each other.$

Exercise $\PageIndex{57}$

Approximate area

$A tubelike shape formed in a half-circle. The inner circle portion's radius is 8ft. The thickness of the tube is 2ft.$

Answer: 56.52 sq ft

Exercise $\PageIndex{58}$

Approximate area

$A triangle with a half-circle on top, resembling an ice cream cone. The triangle's height is 30in, and the circle's radius is 16in.$

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