Lesson 16: Practice Problems

Problem 1

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

  1. Rectangular prism with dimensions 5, 8, 10.
  2. Base is a right triangle with sides 6, 8, 10, prism height 15.
  3. Rectangular prism with dimensions 5, 13, 4.
  4. Base is a right triangle with sides 5, 12, and 13, prism height is 8.
  5. Base is a triangle with sides 6, 5, 5 and height perpendicular to the 6 side is 4, prism height 12.

Problem 2

Here is the base of a prism.

A rectangle with a square cut out of the middle of the bottom side is indicated. The rectangle has vertical side lengths of 5 centimeters and horizontal side lengths of 8 centimeters. The square cut out from the bottom is 2 centimeters on each side, making the bottom horizontal side 3 centimeters on one side of the square and 3 centimeters on the other side of the square.

  1. If the height of the prism is 5 cm, what is its surface area? What is its volume?

  2. If the height of the prism is 10 cm, what is its surface area? What is its volume?

  3. When the height doubled, what was the percent increase for the surface area? For the volume?

Problem 3

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

  1. Determining the amount of paint needed to paint a barn.

  2. Determining the monetary value of a piece of gold jewelry.

  3. Filling an aquarium with buckets of water.

  4. Deciding how much wrapping paper a gift will need.

  5. Packing a box with watermelons for shipping.

  6. Charging a company for ad space on your race car.

  7. Measuring the amount of gasoline left in the tank of a tractor.

Problem 4 From Unit 6 Lesson 11

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.

A rectangular prism.

Problem 5 From Unit 3 Lesson 13

B is the intersection of line  and line . Find the measure of each of the angles.

Two lines and two rays that intersect at point B creates 6 angles. Line AC is slanted downward and to the right and line ED is slanted upward and to the right. Ray BG is drawn between line segment BD and line segment BC. Angle GBC that is formed measures 65 degrees. Ray BF is drawn between line segment BC and line segment BE. Angle FBE that is formed measures 20 degrees. Angle ABE is labeled 110 degrees.

  1. The measure of angle

  2. The measure of angle

  3. The measure of angle

  4. The measure of angle

  5. The measure of angle

Problem 6 From Unit 4 Lesson 9

Write each expression with fewer terms.