Unit 3 - Study Guide

Answers

Questions 1 & 2

The Pythagorean Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

The Pythagorean Theorem can be represented by the equation a2 + b2 = c 2, where a and b are the length of the legs of the triangle, and c is the length of the hypotenuse.

Question 3

Use what you know about the Pythagorean Theorem to label the sides of the following triangle.

hypotenuseleg

leg

Question 4

Is a triangle with the lengths 7, 24, and 25 a right triangle. Why or why not. Show work to indicate how you got your answer.Use the Pythagorean Theorem to determine if this is a right triangle.72 + 242 = 252

49 + 576 = 625625 = 625The sum of the squares of the legs is equal to the square of the hypotenuse, so it is a right triangle.

Question 5

A football field is 360 feet by 45 feet. How long is the walk from one corner diagonally to the opposite corner?

360 ft

45 ft

452 + 3602 = c2

2025 + 129600 = c2

131625 = c2

362.8 ft = c

Question 6

Using the illustration below, what is the approximate height of the hot air balloon?

a2 + 13252 = 20002

a2 + 1755625 = 4000000

a2 = 2244375

a = 1498.1 ft

Question 7

A rectangle has a diagonal 25 inches long and a width of 6 inches. What is the length of the rectangle?

6 in25 in

62 + b2 = 252

36 + b2 = 625

b2 = 589

b = 24.3 in.

Question 8

Which of the following measures are valid measures of the sides of a right triangle? Explain your reasoning.

A. 3, 4, 7B. 5, 12, 13C. 20, 21, 28D. 12, 37, 34

5, 12, and 13 are valid measures of a right triangle because they form a Pythagorean Triple

Question 9A spider has taken up residence in a small cardboard box which measures 2 inches by 4 inches by 4 inches. What is the length, in inches, of a straight spider web that will carry the spider from the lower right front corner of the box to the upper left back corner of the box?

• = • 2

Question 10

A package is in the shape of a cube. The height of the package is 10 inches. What is the diagonal length of the package?

10 in = 2

Question 11

Find the length of the missing side.

3 in

5 in

a2 + b2 = c2

32 + 52 = c2

9 + 25 = c2

34 = c2

5.8 in = c

Questions 12 & 13Solve for y: 2 = 16y3 = 8y = y = 2

Solve for z: 3 = 108 = 36z = Z = 6

Questions 14, 15, & 16Explain what the word volume means.The measure of the space occupied by a solid

How does the volume of a cylinder compare to the volume of a cone?The volume of a cylinder is three times greater than the volume of a cone How does the volume of a cylinder and cone compare to the volume of a sphere?The volume of a sphere is double the volume of a cone and 2/3rd the volume of a cylinder.

Question 17

A candle maker uses a cylinder mold, which is 18 inches tall and has a radius of 1 inch. What is the volume of the candle mold?

18 in.

r = 1 in.

V = 18 V = 56.52 in3

Question 18

A party hat is in the shape of a cone with a radius of 3 in. and a height of 5 in. What is the volume of the party hat?

r = 3 in.

5 in.

3 3

V = 15 and 47.1 in3

Question 19

What is the volume of a beach ball with a radius of 12 centimeters?

r = 12 cm

3 3

V = 2304 and 7234.6 cm3

Question 20

What is the volume of the following cone?

3 3

V = 41.6 and 130.8 mm3

Question 21

1. Find the volume of the sphere shown below.

Radius is 2in

Find the volume of the sphere shown below.

3 3

V = 10.6 and 33.5 in3

Question 22

Find the volume of the cylinder below.

V = 137.4 in3

Question 22

Find the volume of the cylinder below in terms of pi.

V = V = 43.75 in3

If you are finding the volume “in terms of pi”, DO NOT multiply by 3.14.

Question 23

The volume of a cylinder is 12.56 . If the height of the cylinder is 1 m, what is its diameter?

1Multiply 3.14 by 1Divide both sides by 3.14 to isolate r 24 = r2 Find the square root of 4r = 2 m So the diameter is 4 m

r = ? m

h = 1 m

Question 24

What are the two methods of finding the distance between two points?

Given two points, you can always plot them, draw the right triangle, and then find the length of the hypotenuse. The length of the hypotenuse is the distance between the two points. Another way to find the distance between two points is algebraically with a formula.

Question 25

What is the distance between P1 and P2?

9 units

6 units

The legs are 6 and 9, now I can find the distance by finding the hypotenuse of the triangle:

a2 + b2 = c2

62 + 92 = c2

36 + 81 = c2

117 = c2

10.8 = c

Question 26

What is the distance between P1 and P2?

3 units

4 units

The legs are 3 and 4, now I can find the distance by finding the hypotenuse of the triangle:

a2 + b2 = c2

32 + 42 = c2

9 + 16 = c2

25 = c2

5 = c

Question 27

Given points C(-6, 10) and D(-3, -2), what is the length of CD? I can use the distance formula:d = d = d = d = d = CD = 12.4

Question 28

Given points S(-4, -2) and T(-1, 0), what is the length of ST?I can use the distance formula:d = d = d = d = d = ST = 3.6