Illustrative Mathematics | v.360 Curriculum

Problem 1

Edge lengths are given in units. Find the surface area of each prism in square units.

Prism A, rectangular prism with dimensions 5, 8, 10. — A

Prism B, base is a right triangle with sides 6, 8, 10, prism height 15. — B

Prism C, rectangular prism with dimensions 5, 13, 4. — C

Prism D, base is a right triangle with sides 5, 12, and 13, prism height is 8. — D

Prism E, base is a triangle with sides 6, 5, 5 and height perpendicular to the 6 side is 4, prism height 12. — E

Problem 2

ForLesson 8: Slicing Solids

Priya says, “No matter which way you slice this rectangular prism, the cross-section will be a rectangle.” Mai says, “I’m not so sure.” Describe a slice that Mai might be thinking of.

Problem 3

ForLesson 18: Using Equations to Solve for Unknown Angles

\(B\) is the intersection of line \(AC\) and line \(ED\). Find the measurement of each of the angles.

Angle \(ABF\)
Angle \(ABD\)
Angle \(EBC\)
Angle \(FBC\)
Angle \(DBG\)

Two lines and two rays that intersect at point B creating 6 angles.

Problem 4

Select all the situations where knowing the volume of an object would be more useful than knowing its surface area.

Determining the amount of paint needed to paint a barn.
Determining the monetary value of a piece of gold jewelry.
Filling an aquarium with buckets of water.
Deciding how much wrapping paper a gift will need.
Packing a box with watermelons for shipping.
Charging a company for ad space on your race car.
Measuring the amount of gasoline left in the tank of a tractor.

Problem 5

Here is the base of a prism.

An 8-sided figure, all angles right, lengths, centimeters. From the first vertex, a segment extends 8 right, then 5 down, then 3 left, then 2 up, then 2 left, then 2 down, then 3 left, then 5 up.

If the height of the prism is 5 cm, what is its surface area? What is its volume?
If the height of the prism is 10 cm, what is its surface area? What is its volume?
When the height doubled, what was the percent increase for the surface area? For the volume?

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