Volume Review

An engineer creates a solid steel for an engine. The part has a volume of 1500 cm3. Steel can be purchased for $0.40 per kg, and has a density of 7.95 g/cm3 .If the engineer makes 300 of these parts, what is the cost of the steel to the nearest dollar?

• $120

• $75

• $1,431

• $4,770

Answer explanation

Find mass by multiplying density times volume.

Then convert grams to kilograms.

Then multiply by the cost and the number of parts the engineer is purchasing.

Tags

CCSS.HSG.MG.A.2

A table shows the square footage of various high schools in a city and the number of students who attend that school.

What is the population density of the school that has the lowest number of students per square foot?

(a)  

Answer explanation

population density = population/area

students per square footage

Tags

CCSS.6.RP.A.3B

A container of old fashion oats has a diameter of 20 cm and can hold 1570 cubic centimeters of oats. Approximately what is the height of the container?

• 10 cm

• 12 cm

• 5 cm

• 25 cm

Answer explanation

1570 = π(10)²h

Inverse operations to solve for height.

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

Picture this: You have four figures that have the same height and the same base area: triangular pyramid, rectangular prism, cylinder, and a triangular prism. According to Cavalieri's Principle, which figures have equal volumes?

• triangular prism and triangular pyramid

• rectangular prism and triangular prism

• cylinder and rectangular prism

• rectangular prism, cylinder and triangular prism

• All of the above

Answer explanation

Prisms and cylinders' parallel cross sections have the same areas throughout their entire height where as the pyramid's parallel cross sections decrease in size as you move up the figure.

A pyramid has a height of 5 inches and a volume of 70 cubic inches. Which of the following figures could be the base for this pyramid? Select all that apply.

• a square with side length 7

• a 6-inch by 7-inch rectangle

• a 5-inch by 8-inch rectangle

• a pentagon with an area of 40 square inches

Tags

CCSS.HSG.GMD.A.3

Find the volume of the mailbox to the nearest cubic millimeter.

• 1294 cubic mm

• 594 cubic mm

• 700 cubic mm

• 944 cubic mm

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

Find the volume of the composite figure to the nearest cubic centimeter.

• 18,750 cubic cm

• 20,258 cubic cm

• 17,242 cubic cm

• 1,508 cubic cm

Tags

CCSS.5.MD.C.5C

Jenny says that the two prisms DO NOT have the same volume because even though they are the same height, the cross sections are not the same.

Rene disagrees. He says that the two cross sections while not the same shape, have the same area, so the volumes must be equal.

Who is correct?

• Rene

• Jenny

Answer explanation

Cavalieri's Principle

Tags

CCSS.7.G.B.6

A 3-D solid is formed by rotating the rectangle shown at the right about the vertical line. The dimensions of the rectangle are stated in inches. What is the volume of the solid formed by this rotation, in cubic inches?

• 45 in³

• 45π in³

• 90 in³

• 90π in³

Tags

CCSS.HSG.GMD.A.3

CCSS.8.G.C.9

What is the volume of this figure?

• 30 m³

• 10 m³

• 20 m³

• 50 m³

Tags

CCSS.HSG.GMD.A.3