Pythagorean Theorem Missing Sides, Volume Cones, Spheres, Cylinders

How do you find the volume of a cylinder?

• V= ^1/₃ πr²h

• V= ^4/₃ πr²

• V= ^4/₃ πr³

• V= πr²h

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

How do you find the volume of a cone?

• V= ^1/₃ πr²h
• V= ^4/₃ πr²h
• V= ^4/₃ πr³
• V= πr²h

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

How do you find the volume of a sphere?

• V= ^1/₃ πr²h
• V= ^4/₃ πr²h
• V= ^4/₃ πr³
• V= πr²h

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

The figure shown below is composed of a rectangular prism and two half cylinders. Which is closest to the volume of the figure?

• 781 cm³
• 706 cm³
• 631 cm³
• 593 cm³

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

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.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

A rancher wants to cut a metal cylinder in half to use as a watering trough as shown.
If the cylinder has a diameter of 5 feet and a length of 9 feet, which value is closest to the volume of the trough in cubic feet? Use π = 3.14.

• 176.6 ft³
• 141.3 ft³
• 88.3 ft³
• 70.7 ft³

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

A hollow glass cone is filled with perfume and placed inside of a hollow cylindrical container with the same height and diameter as the cone. The cylinder will then be filled with packing material. If the cone occupies 60 cm³ of space, how many cubic centimeters of packing material will be needed?

• 30

• 60

• 120

• 180

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

A rectangular glass window measuring 9" by 11" is divided into two equivalent right triangles by a diagonal brace. What is the length of the diagonal brace?

• 9 inches

• 12 inches

• 15 inches

• 21 inches

Tags

CCSS.8.G.B.8

A water tank is a compound shape consisting of a cylinder and an inverted cone as shown below. The cylinder has a diameter of 8 meters (m) and a height of 6 m. The cone has a diameter of 8 m and a height of 3 m. What is the total volume of the tank in cubic meters? (Use π = 3.14)

• 200.72

• 301.44

• 351.68

• 452.92

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

A balloon that is tied to a stake in the ground is being blown sideways by the wind. The length of the string from the stake to the balloon is 26 feet, and the distance from the stake to a point directly under the balloon is 24 feet. If x is the distance in feet from the balloon to the ground, what is the value of x?

• 2

• 4

• 10

• 25

Tags

CCSS.8.G.B.7