Chapter 7 Test Review: Pythagorean Theorem, Distance Formula & Volume

A sphere has a volume of 0.52. What is the radius of the sphere?

0.5

A sphere has a volume of 4.19. What is the radius of the sphere?

1

A sphere has a volume of 14.13. What is the radius of the sphere?

1.5

(-3, -1) (5, -7)

10

(6, -2) (-2, 4)

10

Find the distance between the points (7,2) and (1,10).

10 units

Find the distance between the points (9,6) and (1,0).

10 units

(-3, -4) (5, 5)

12

Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 16 miles. If the two airplanes are 20 miles apart, how far has the eastbound airplane traveled?

12 miles

(0, 5) (12, 3)

12.2

The floor of a rectangular living room is 5 meters by 12 meters. What is the distance between opposite corners of the living room?

13 meters

49.5

A cylindrical glass is 7 inches high and has a diameter of 3 inches. How many cubic inches of water can the glass hold when filled to the top?

61575.2

A cylindrical grain silo is 100 feet high and has a radius of 14 feet. How many cubic feet of grain can be kept in the silo?

5.3

A cylindrical oil drum is 2.1 meters high and has a radius of 0.9 meter. What is the volume of the oil drum.

1,539.4

A cylindrical water tower is half full of water. How much water is in the tower if it measures 20 feet high and has a radius of 7 feet?

113.177

A football field is 100 yards long and 53 yards wide, what is the distance of the diagonal of the field?

113.177 yards

A football field is 100 yards long and 53 yards wide, what is the distance of the diagonal of the field?

40

From her house, Leah rode 8 miles south, and then 15 miles west. she then rode back home in a straight path. What was the total distance Leah rode her bike? (Draw a picture, and watch what the question is asking!)

16

In Lanberry, the library is due south of the courthouse and due west of the community swimming pool. If the distance between the library and the courthouse is 12 miles and the distance between the courthouse and the city pool is 20 miles, how far is the library from the community pool?

No

Is this a right triangle: a=4, b=6, c=9

1436

Jose measures the diameter of a ball as 14 inches. How many cubic inches of air can the ball hold, to the nearest tenth ?

24.04

Marisa wants to use a fence to divide her square garden in half diagonally. If each side of her garden is 17 feet long, how long will the fence have to be? (Just the diagonal piece.) Draw a picture to help!

10

On a sunny day, the oak tree in Elijah's yard casts a 24 foot shadow. If the distance from the end of the shadow to the top of the tree is 26 feet, how tall is the actual tree?

a triangle where one angle is guaranteed to be 90 degrees.

Right Triangle

11.2

Solve for the missing side length

A²+ B² = C²

The Pythagorean Theorem

12,120.9

The diameter of a basketball is 28.5 inches. Find the volume of the basketball.

13

The floor of a rectangular living room is 12 meters by 5 meters. What is the distance between opposite corners of the living room?

hypotenuse

The longest side of a right triangle

4.2

Find the volume of a ping-pong ball with a radius of 1 inch.

452.4

Find the volume of half of a sphere.

167.6

Find the volume of the cone.

201.1

Find the volume of the cone.

340.3

Find the volume of the cone.

16,964.60

Find the volume of the cylinder.

56.5

Find the volume of the cylinder.

169.6

Find the volume of the dad's mug.

3,053.6

Find the volume of the sphere.

904.8

Find the volume of the sphere.

3052.08

Find the volume of the sphere. Round to the nearest tenth. Use 3.14 for pi.

44.6

Find the volume of the sphere. Round to the nearest tenth. Use 3.14 for pi.

904.32

Find the volume of the sphere. Round to the nearest tenth. Use 3.14 for pi.

6.3

Find the volume of the waffle cone.

3,015.9

Find the volume.

10

a=6 b=8 c=?

69.3

a=65, b=?, c=95

25

a=7 b=24 c=?

60

a=80, c=100, b=?

70

Find the missing length of the right triangle.

15.620

Find the missing side: a=12 b=10

4

Find the missing side: a=3, c=5

(10, 14) (-8, 14)

18

A sphere has a volume of 33.49. What is the radius of the sphere?

2

A sphere has a volume of 65.42. What is the radius of the sphere?

2.5

(-5, -3) (-3, -5)

2.8

(12, 6) (-8, 18)

23.3

(12, -12) (5, 12)

25

A sphere has a volume of 113.04. What is the radius of the sphere?

3

A sphere has a volume of 179.50. What is the radius of the sphere?

3.5

A sphere has a volume of 267.95. What is the radius of the sphere?

4

A sphere has a volume of 381.51. What is the radius of the sphere?

4.5

(3, 2) (6, 6)

5

A sphere has a volume of 523.33. What is the radius of the sphere?

5

Molly bicycles 3 miles west to get from her house to school. After school, she bicycles 4 miles north to her friend Russell's house. How far is Molly's house from Russell's house, measured in a straight line?

5 miles

Find the distance between the points (4,2) and (1,6).

5 units

Find the distance between the points (6,4) and (3,8).

5 units

(-5, 2) (0, 4)

5.4

A sphere has a volume of 696.56. What is the radius of the sphere?

5.5

(0, -2) (3, 3)

5.8

(2, -1) (2, 5)

6

A sphere has a volume of 904.32. What is the radius of the sphere?

6

From his home, Martin would have to walk due north to get to his friend Erica's house and due east to get to his friend Tara's house. It is 8 kilometers from Martin's house to Tara's house and a straight-line distance of 10 kilometers from Erica's house to Tara's house. How far is Martin's house from Erica's house?

6 kilometers

A sphere has a volume of 1149.76. What is the radius of the sphere?

6.5

A sphere has a volume of 1436.03. What is the radius of the sphere?

7

Find the distance between (2,3) and (1,10)

7.071

(-4,-2) (1, 3)

7.1

(-1, -11) (-1, -3)

8

(0, 3) (0, 12)

9

13

Find the missing side: a=5, b=12

17.888

Find the missing side: b=16 c=24

15.6

A piece of lumber is leaning against a wall. The top of the lumber hits the wall 12 feet above the ground. The bottom of the lumber is 10 feet away from the wall. About how long is the piece of lumber? (Draw a picture to help.)

263.9

A pile of sand is shaped like a cone. If the height is 7 meters and the radius is 6 meters, how many cubic meters of sand are in the pile?

30

A traffic helicopter flies 5 miles due north, and then 12 miles due east. Then the helicopter flies a straight path back to where it started. How far did the helicopter travel altogether? (*After you draw your picture, watch what the question is asking!)

(^▽^)/＜Challenge!! The class of math is mapped on a coordinate grid with the origin being at the center point of the hall. Mary's seat is located at the point (-4, 7) and Betty's seat is located at (-2, 5). How far is it from Mary's seat to Betty's seat? A. √13 units B. 2√2 units C. 5 units D. 7 units

B. 2√2 units

(^▽^)/＜Challenge!! If the legs of a right triangle are x, (2x - 1) and its hypotenuse is (2x + 1), what is the value of x? A. 2 B. 4 C. 6 D. 8

D. 8

20

Devon is walking home from school one day and decides to take a shortcut. He walks diagonally across a rectangular vacant lot. The length of the lot is 30 yards, and the width of the lot is 40 yards. How many yards did Devon save by taking the shortcut? (Watch what the question is asking you for!)

12

Find b: a=5 b=? c=13

2373.84

Find the combined volume of the figure. (Hint: volume of a cylinder + volume of a hemisphere)

7.616

Find the distance between (-5,-4) and (-2, 3)

9.849

Find the distance between (0,0) and (9, 4)

11.180

Find the distance between (0,2) and (5, 12)

32.388

Find the distance between (2,24) and (7,56)

7.071

Find the distance between (2,3) and (1, 10)

4.123

Find the distance between (2,9) and (1,5)

8.602

Find the distance between (4,8) and (9,15)

17.5

Find the length of the diagonal line inside the rectangular prism.

31.2

Find the length of the diagonal line inside the rectangular prism.

10

Find the missing length of the right triangle.

14.3

Find the missing length of the right triangle.

6.3

Find the missing length of the right triangle.

legs

The sides that form the right angle in a right triangle

18

The size of a television is determined by the length of its diagonal. If a 30" plasma TV has a LENGTH of 24 inches, what is the HEIGHT? Draw a picture to help.)

20

The volume of a cone is 60π inches3. If the radius of the cone is 3 inches, what is the height?

10

The volume of a cylinder is 810π cm3. If the radius is 9 cm, what is the height?

36

What is the perimeter of this triangle if the two legs are 9 cm and 10 cm?

5881.1

What is the volume of a cone with a radius of 12 inches and a height of 39 inches?

769.7

What is the volume of a cylinder with a height of 20 yards and a diameter of 7 yards?

170.2

What is the volume of half the cone?

14.1

What is the volume of the baseball when the diameter is approximately 3 inches.

2177.9

What is the volume of the can? (Hint: Be careful. You are given the diameter)

461.8

What is the volume of the cone?

2,010.6

What is the volume of the cylinder?

28.26

What is the volume of this cone with a height and radius of 3? Use 3.14 for pi.

27.7

What is the volume of this cone? Use 3.14 for pi.

17

Whenever he visits Cedarburg, Marlon has to drive 8 miles due north from home. Whenever he visits Lexington, he has to drive 15 miles due east from home. How far apart are Cedarburg and Lexington, measured in a straight line?

10

Which is the appropriate length of the hypotenuse of the right triangle?

4.8

Which is the appropriate length of the hypotenuse of the right triangle?

Yes

Would these sides form a right triangle? 24, 25, 7

No

Would these sides form a right triangle? 50, 70, 50

Yes

Would these three sides form a right angle 8, 15, 17

right triangle

a triangle with a 90 degree angle

23.4

a=18, b=15, c=?

5

a=3 b=4 c=?

73.3

b=95, c=120, a=?

Hypotenuse

c, and the longest side of a right triangle, opposite the right angle

10

c=26, a=24, b=?

The longest side of a right triangle. It is always opposite of, and never is a part of, the right angle.

hypotenuse

Leg

labeled a and b, the two sides of the right triangle that join to form the right angle

Either of the two shortest sides of a right triangle, they meet at a common vertex to form a right angle.

leg

The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

pythagorean theorem

An angle of exactly 90 degrees.

right angle