Metric System Measurements

Podcast Beta

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the formula for the volume of a cube?

$V = s^3$ (correct)

$V = 4s$

$V = s^2$

$V = 6s$

Which formula represents the surface area of a rectangular prism?

$SA = 6s^2$

$SA = 2Lw + 2h$

$SA = L^2 + w^2 + h^2$

$SA = 2lw + 2lh + 2wh$ (correct)

What is the formula for the circumference of a circle?

$C = rac{1}{2}eta d$

$C = eta r^2$

$C = eta d$

$C = 2eta r$ (correct)

How do you calculate the sum of the interior angles of a pentagon?

540° Signup and view all the answers

What is the formula for calculating simple interest?

I = Prt Signup and view all the answers

How is percentage calculated in the formula P = R% of B?

P = B * R/100 Signup and view all the answers

What is the volume of 1 cubic yard in cubic feet?

27 ft³ Signup and view all the answers

If the highest value in a data set is 15 and the lowest is 5, what is the range?

10 Signup and view all the answers

What is the formula to calculate the area of a triangle?

A = (b * h)/2 Signup and view all the answers

What is the correct Pythagorean Theorem equation?

a² + b² = c² Signup and view all the answers

What is the approximate value of 1 kilogram in pounds?

2.2 lb Signup and view all the answers

In the formula for compound interest A = P (1 + r/n)^(nt), what does 'n' represent?

The number of times interest is compounded per year Signup and view all the answers

How many inches are there in 1 meter?

39.37 in Signup and view all the answers

What is the equivalent of 1 gallon in liters?

3.7854 L Signup and view all the answers

If 1 ton is approximately 0.9072 metric tons, how many tons are there in 1 metric ton?

1.1023 tons Signup and view all the answers

What is the conversion factor for 1 square yard to square feet?

9 ft² Signup and view all the answers

How many cups are there in 1 quart?

4 cups Signup and view all the answers

How many feet are in 1 mile?

5280 ft Signup and view all the answers

If 1 acre is equivalent to how many square meters?

4047 m² Signup and view all the answers

How many ounces are there in 1 pint?

16 oz Signup and view all the answers

Study Notes

Metric System

The metric system uses the following prefixes: Kilo, Hecto, Deka, UNIT, Deci, Centi, Milli.
The metric system is used to measure: meters (length), liters (volume), grams (mass).

Length

1 inch (in) = 2.54 centimeters (cm)
1 foot (ft) = 30.48 cm = 0.3048 meters (m)
1 yard (yd) = 91.44 cm = 0.9144 m
1 mile (mi) ≈ 1.61 kilometers (km)
1 millimeter (mm) ≈ 0.03937 in
1 centimeter (cm) ≈ 0.3937 in
1 meter (m) ≈ 1.0936 yd = 3.2808 ft
1 kilometer (km) ≈ 0.6214 mi
1 foot (ft) = 12 inches (in)
1 yard (yd) = 3 ft
1 yard (yd) = 36 in
1 mile (mi) = 5280 ft
1 mile (mi) = 1760 yd

Area

1 square foot (ft2) = 144 square inches (in2)
1 square yard (yd2) = 9 ft2 = 1296 in2
1 square mile (mi2) = 27,878,400 ft2 = 3,097,600 yd2
1 acre = 43,560 ft2
1 square mile (mi2) = 640 acres
1 square inch (in2) ≈ 6.45 cm2
1 square foot (ft2) ≈ 0.093 m2
1 square yard (yd2) ≈ 0.836 m2
1 square mile (mi2) ≈ 2.59 km2
1 acre ≈ 4,047 m2

Volume

1 pint (pt) = 16 ounces (oz)
1 quart (qt) = 2 pt
1 gallon (gal) = 4 qt
1 pint (pt) = 2 cups
1 cup = 8 oz
1 gallon (gal) = 128 oz
1 cubic foot (ft3) ≈ 7.48 gal
1 cubic yard (yd3) ≈ 201.97 gal
1 gallon (gal) ≈ 231 in3
1 cubic foot (ft3) of fresh water ≈ 62.5 lb
1 cubic foot (ft3) of salt water ≈ 64 lb
1 cubic centimeter (cm3) = 1 milliliter (mL) = 1 gram (g) = 1000 mm3
1 cubic decimeter (dm3) = 1000 cm3 = 1 liter (L) = 1 kilogram (kg)
1 cubic meter (m3) = 1000 dm3 = 1 kiloliter (kL) = 1,000 L
1 liter (L) ≈ 1.06 qt
1 gallon (gal) ≈ 3.7854 L
1 quart (qt) ≈ 0.9464 L
1 ounce (oz) ≈ 29.5735 mL
1 cubic foot (ft3) = 1728 in3
1 cubic yard (yd3) = 27 ft3
1 cubic foot (ft3) ≈ 0.02832 m3
1 cubic yard (yd3) ≈ 0.7646 m3

Weight

1 pound (lb) = 16 ounces (oz)
1 ton (T) = 2,000 lb
1 ton (T) ≈ 0.9072 metric ton (t)
1 kilogram (kg) = 1000 grams (g)
1 metric ton (t) = 1,000 kg
1 kilogram (kg) ≈ 2.2 lb
1 ounce (oz) ≈ 28 g

Time

1 minute (min) = 60 seconds (sec)
1 hour = 60 min
1 day = 24 hours
1 year = 365 days

Percentage

To find a percentage, divide the part by the whole and multiply by 100.
Percentage = Rate * Base

Math Formulas

Slope-Intercept Form: 𝑦 = 𝑚𝑥 + 𝑏 , where 𝑚 is the slope and 𝑏 is the y-intercept.
Slope Formula: 𝑚 = (𝑦2 − 𝑦1) / (𝑥2 − 𝑥1)
Celsius to Fahrenheit Conversion: 𝐹= (9/5)𝐶 + 32
Fahrenheit to Celsius Conversion: 𝐶 = (5/9)(𝐹 − 32)
Simple Interest: 𝐼 = 𝑃𝑟𝑡 , where 𝐼 is interest, 𝑃 is principle, 𝑟 is rate and 𝑡 is time
Compound Interest: 𝐴 = 𝑃(1 + 𝑟/𝑛) 𝑛𝑡 , where 𝐴 is the final amount, 𝑃 is the principle, 𝑟 is the rate, 𝑡 is the time, and 𝑛 is the number of times compounded per year.
Future Value: 𝐴 = 𝑃 + 𝐼
Present Value: 𝑃 = 𝐴 / (1 + 𝑟/𝑛) 𝑛𝑡
Range: highest value – lowest value
Pythagorean Theorem: 𝑎2 + 𝑏 2 = 𝑐 2

Geometry Formulas

Area of a Rectangle: 𝐴 = 𝐿𝑤, where 𝐿 is length and 𝑤 is width.
Perimeter of a Rectangle: 𝑃 = 2(𝐿) + 2(𝑤)
Area of a Square: 𝐴 = 𝑠2, where 𝑠 is the side length.
Perimeter of a Square: 𝑃 = 4𝑠
Area of a Parallelogram: 𝐴= 𝑏ℎ, where 𝑏 is the base and ℎ is the height.
Perimeter of a Parallelogram: 𝑃 = 2(𝑏) + 2(ℎ)
Area of a Triangle: 𝐴 = (1/2) 𝑏ℎ, where 𝑏 is the base and ℎ is the height.
Perimeter of a Triangle: 𝑃 = 𝑠1 + 𝑠2 + 𝑠3, where 𝑠 represents the side lengths.
Area of a Trapezoid: 𝐴 = (1/2) ℎ(𝑎 + 𝑏), where 𝑎 and 𝑏 are the parallel sides and ℎ is the height.
Perimeter of a Trapezoid: 𝑃 = 𝑠1 + 𝑠2 + 𝑠3 + 𝑠4, where 𝑠 represents the side lengths.
Area of a Circle: 𝐴 = 𝜋𝑟 2, where 𝜋 is the constant (approximately 3.14) and 𝑟 is the radius.
Circumference of a Circle: 𝐶 = 𝜋𝑑, where 𝜋 is the constant (approximately 3.14) and 𝑑 is the diameter.
Circumference of a Circle: 𝐶 = 2𝜋𝑟, where 𝜋 is the constant (approximately 3.14) and 𝑟 is the radius.
Volume of a Cube: 𝑉 = 𝑠3, where 𝑠 is the side length.
Surface Area of a Cube: 𝑆𝐴 = 6𝑠 2, where 𝑠 is the side length.
Volume of a Sphere: 𝑉 = (4/3)𝜋𝑟 3, where 𝜋 is the constant (approximately 3.14) and 𝑟 is the radius.
Surface Area of a Sphere: 𝑆𝐴 = 4𝜋𝑟 2, where 𝜋 is the constant (approximately 3.14) and 𝑟 is the radius.
Volume of a Rectangular Prism: 𝑉 = 𝐿𝑤ℎ, where 𝐿 is the length, 𝑤 is the width, and ℎ is the height.
Surface Area of a Rectangular Prism: 𝑆𝐴 = 2𝐿𝑤 + 2𝑤ℎ + 2𝐿ℎ, where 𝐿 is the length, 𝑤 is the width, and ℎ is the height.
Volume of a Cylinder: 𝑉 = 𝜋𝑟 2 ℎ, where 𝜋 is the constant (approximately 3.14), 𝑟 is the radius, and ℎ is the height.
Surface Area of a Cylinder: 𝑆𝐴 = 2𝜋𝑟ℎ + 2𝜋𝑟 2, where 𝜋 is the constant (approximately 3.14), 𝑟 is the radius, and ℎ is the height.
Volume of a Cone: 𝑉 = (1/3)𝜋𝑟 2 ℎ, where 𝜋 is the constant (approximately 3.14), 𝑟 is the radius, and ℎ is the height.
Surface Area of a Cone: 𝑆𝐴 = 𝜋𝑟 + 𝜋𝑟√𝑟 2 + ℎ 2 , where 𝜋 is the constant (approximately 3.14), 𝑟 is the radius, and ℎ is the height.
Sum of Interior Angles of a Polygon: (𝑛 − 2) ∙ 180°, where 𝑛 is the number of sides.

Properties of Exponents

𝑎𝑚 ∙ 𝑎𝑛 = 𝑎𝑚+𝑛
𝑎𝑚 / 𝑎𝑛 = 𝑎𝑚−𝑛 , 𝑎 ≠ 0
(𝑎𝑚) 𝑛 = 𝑎𝑚∙𝑛
𝑎−𝑛 = 1 / 𝑎𝑛 , 𝑎 ≠ 0
𝑎0 = 1 , 𝑎 ≠ 0

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

This quiz covers the fundamentals of the metric system, including its prefixes and units for measuring length, area, and volume. Test your knowledge on conversions between metric and imperial units, and understand how to apply metric measurements in various contexts.