8th Grade PSSA: Geo-Pyth and Volume Review

8th Grade PSSA: Geo-Pyth and Volume Review

Pyth and Volume Review

THE PYTHAGOREAN THEOREM

•  $a^2\ +\ b^2\ =\ c^2$  

• Used only for right triangles

• a = shortest  leg, b = longest leg, c = hypotenuese (longest side the slide)

Multiple Choice

A rectangular field is 50 yards wide and 100 yards long. Patrick walks diagonally across the field. How far does he walk?

• 111.8 yards
• 115 yards
• 127.3 yards
• 119 yards

Multiple Choice

_{^{Find the missing side}}

• 37
• 17.66
• 6
• 312

Multiple Choice

_{^{Find the missing side}}

• 9
• 41
• 6.4
• 3

Multiple Choice

Find the length of the missing side. 

• 20 in.
• 68 in.
• 16 in.
• 80 in.

Multiple Choice

Determine the length of the missing side.

• 7

• 8

• 17

• 23

Multiple Choice

Name the longest side of a right triangle.

• leg a
• leg b
• leg 
• hypotenuse

Multiple Choice

Side c on a right triangle is ALWAYS the longest.

• true

• false

Multiple Choice

Sides a and b are called legs.

• true

• false

Multiple Choice

The Pythagorean Theorem ONLY works on which triangle? 

• obtuse
• scalene
• isosceles
• right

Multiple Choice

Side a on a right triangle is ALWAYS the longest side.

• true
• false

Is a triangle, obtuse, acute, or right??

• Use the Pythagorean theorem

•  $a^2\ +\ b^2\ =c^2$  if after plugging in your traingles sides to the formula and  equal than right triangle

• If  $a^2\ +b^2\ >\ c^2$  then acute.  Note the hypotenuese or  $c^2\ is\ small\ or\ acute$  

• If  $a^2\ +\ b^2\ <\ c^2$  then obtuse.  Note the  $c^2\$  is larger or obtuse

Multiple Choice

What type of triangle is this?

• Right Triangle

• Acute Triangle

• Obtuse Triangle

Multiple Choice

What kind of triangle is this?

• Right Triangle

• Acute Triangle

• Obtuse Triangle

Multiple Choice

What type of triangle is this?

• Right Triangle

• Acute Triangle

• Obtuse Triangle

Multiple Choice

What kind of triangle is this?

• Right Triangle

• Acute Triangle

• Obtuse Triangle

Volume Review

• Cylinder: V =  $\pi r^2h$  

• Cones:  V = (1/3) $\pi r^2h$  

• Sphere:  V = (4/3) $\pi r^3$  

Volume Continued:

• Always locate and label you variable:

• h = height, v = volume, r = radius, $\pi$  $\approx$   3.14

• Do this before attempting to solve a problem

IMPORTANT NOTE:

• If you are given the diameter, you must divide it by 2 to get the radius

• The diameter goes across the entire sphere like the axis of the earth

• The radius is more like a slice of pizza it only goes halfway

Multiple Choice

The volume of a cone is   $2,307.9\ mm^3$  and the height is  $5\ mm$ .  What is the radius? Use  $\pi\approx3.14.$ 

•  $r=147\ mm$  

•  $r=47\ mm$  

•  $r=\ 441\ mm$  

•  $r=21\ mm$  

Multiple Choice

The volume of a cone is  $1,436.03\ ft^3.\ \$  It's radius is  $7\ ft.$  Solve for the height. Use  $\pi\approx3.14.$ 

•  $h=12\ ft$  

•  $h=28\ ft$  

•  $h\approx3.5\ ft$  

•  $h\ =\ 14\ ft$  

Multiple Choice

The volume of a cylinder is $226.08\ ft^3$  and the radius is  $6\ ft.$  What is the height? Use  $\pi\approx3.14.$ 

•  $h\ =9\ ft$  

•  $h=36\ ft$  

•  $h=2\ ft$  

•  $h\ =\ 12\ ft$  

Multiple Choice

If a has cylinder a radius of 4 yd and a volume of 80 $yd^3$ , solve for the height to the nearest tenth. Use  $\pi\approx3.14.$  

• 4,019.2 yds.

• 6.4 yds.

• 1.65yds.

• 1.6 yds.

Multiple Choice

Find the volume of the hemisphere

• 904.3 in³
• 226.1in³
• 113.0 in³
• 452.2 in³

Multiple Choice

Find the volume to the nearest hundredth.

• 12.57 ft³

• 37.68 ft³

• 18.84 ft³

• 6.28 ft³

Multiple Choice

Find the Volume of the Sphere

• 904.32 ft³
• 7,234.56 ft³
• 150.72 ft³

Multiple Choice

Kayla has two spherical balls in her yard (see picture).Which statement about their volumes is true?

• The volume of Ball 2 is twice the volume of Ball 1.
• The volume of Ball 1 is 8 times the volume of Ball 2.
• The volume of Ball 1 is twice the volume of Ball 2.
• The volume of Ball 2 is 8 times the volume of Ball 1.

Multiple Choice

Find the Volume of the Cylinder

• 1178 ft³
• 4712 ft³
• 7069 ft³
• 3534 ft³

Multiple Choice

 Find the volume of the Cylinder

• 7230
• 6621
• 1130
• 907

Finding Distance using the Pythagorean Theorem

• Using your points, connect the two points on your graph to form the hypontaneuse of your right triangle

• Then using your points create a right triangle. It will look like rise and run.

• Count the spaces/blocks (not the lines)

• Use these totals for the legs of your triangle. Leg A = ? Leg B = ?

• Make sure to then plug everything into the Pyth Theorem and solve for C, your distance is the hypoteneuse

Multiple Choice

Find the distance between J and K.

• 8.2
• 7.7
• 9
• 10.2

Multiple Choice

 What is the distance between A & B?

• 4.1
• 5.1

Multiple Choice

Find the distance.

• 9.7
• 10.7
• 11.7
• 12.7

Multiple Choice

What is the distance between the two points?

• 6.3
• 6.5
• 6.7
• 16

Multiple Choice

 What is the distance between A & B?
See Study Guide

• 4.1
• 5.1

Poll

Did this help you to review Volume and Pythagorean Theorem?

• Yes

• No

If you need additional help:

• GO to Youtube and find videos to review

• Check your notes:)