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Exercise Supplement

Module by: Wade Ellis, Denny Burzynski. E-mail the authorsEdited By: Math Editors

Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is an exercise supplement for the chapter "Measurement and Geometry" and contains many exercise problems. Odd problems are accompanied by solutions.

Exercise Supplement

Measurement and the United States System ((Reference))

Exercise 1

What is measurement?

Solution

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

For problems 2-6, make each conversion. Use the conversion table given in Section 9.1.

Exercise 2

9 ft=
yd

Exercise 3

32 oz=
lb

Solution

2 pounds

Exercise 4

1,500 mg =
g

Exercise 5

12,000 lb =
T

Solution

6 tons

Exercise 6

5,280 ft=
mi

For problems 7-23, make each conversion.

Exercise 7

23 yd to ft

Solution

69 feet

Exercise 8

212212 size 12{2 { {1} over {2} } } {}mi to yd

Exercise 9

8 in. to ft

Solution

23=0.666¯  feet23=0.666¯  feet size 12{ { {2} over {3} } =0 "." "66" {overline {6}} " feet"} {}

Exercise 10

51 in. to mi

Exercise 11

3 qt to pt

Solution

6 pints

Exercise 12

8 lb to oz

Exercise 13

5 cups to tbsp

Solution

80 tablespoons

Exercise 14

9 da to hr

Exercise 15

312312 size 12{3 { {1} over {2} } } {} min to sec

Solution

210 seconds

Exercise 16

3434 size 12{ { {3} over {4} } } {} wk to min

The Metric System of Measurement ((Reference))

Exercise 17

250 mL to L

Solution

14=0.2514=0.25 size 12{ { {1} over {4} } =0 "." "25"} {}L

Exercise 18

18.57 cm to m

Exercise 19

0.01961 kg to mg

Solution

19,610 mg

Exercise 20

52,211 mg to kg

Exercise 21

54.006 dag to g

Solution

540.06 g

Exercise 22

1.181 hg to mg

Exercise 23

3.5 kL to mL

Solution

3,500,000 mL

Simplification of Denominate Numbers ((Reference))

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

Exercise 24

Add 8 min 50 sec to 5 min 25 sec.

Exercise 25

Add 3 wk 3 da to 2 wk 5 da

Solution

6 weeks 1 day

Exercise 26

Subtract 4 gal 3 qt from 5 gal 2 qt.

Exercise 27

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

Solution

5 gallons 2 quarts 1 pint

Exercise 28

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

Exercise 29

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

Solution

7 T 1,850 pounds

Exercise 30

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

Exercise 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.

Solution

7 days, 11 hours, 56 minutes, 7 seconds

For problems 32-43, simplify, if necessary.

Exercise 32

18 in.

Exercise 33

4 ft

Solution

1 yard 1 foot

Exercise 34

23 da

Exercise 35

3,100 lb

Solution

1 ton 1,100 pounds

Exercise 36

135 min

Exercise 37

4 tsp

Solution

1 tablespoon 1 teaspoon

Exercise 38

10 fl oz

Exercise 39

7 pt

Solution

3 quarts 1 pint

Exercise 40

9 qt

Exercise 41

2,300 mm

Solution

2.3 meters

Exercise 42

14,780 mL

Exercise 43

1,050 m

Solution

1.05 km

Perimeter, Circumference, Area and Volume of Geometric Figures and Objects ((Reference),(Reference))

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

Exercise 44

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

Exercise 45

Approximate circumference
A circle. The circle's diameter is 1.8cm.

Solution

5.652 sq cm

Exercise 46

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

Exercise 47

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

Solution

104.28568 cu ft

Exercise 48

Exact area
A circle. The circle's diameter is 5m.

Exercise 49

Exact area
A half-circle with radius 0.6in.

Solution

0.18 π π sq in.

Exercise 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 51

Approximate volume
A sphere with radius 8mm.

Solution

267.94667 cu mm

Exercise 52

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

Exercise 53

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

Solution

32 cu cm

Exercise 54

Exact area
A complex shape involving two circles and a circular cutout.

Exercise 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.

Solution

39.48 sq in.

Exercise 56

Exact area
A shape composed of four circles overlapping each other.

Exercise 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.

Solution

56.52 sq ft

Exercise 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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