Lesson 15: Practice Problems

Problem 1

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.

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?

Problem 2

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 3 From Unit 7 Lesson 9

Han draws a triangle with a $50^{\circ}$ angle, a $40^{\circ}$ angle, and a side of length 4 cm as shown. Can you draw a different triangle with the same conditions?

A right triangle with a horizontal side. The angle with the right angle symbol is directly above the horizontal side. The bottom left angle of the triangle measures 40 degrees and the bottom right angle measures 50 degrees. The side opposite the 40 degree angle is labeled 2 point 6 centimeters. The side opposite the 50 degree angle is labeled 3 point 1 centimeters. The horizontal side is labeled 4 centimeters.

Problem 4 From Unit 7 Lesson 3

Angle $H$ is half as large as angle $J$ . Angle $J$ is one fourth as large as angle $K$ . Angle $K$ has measure 240 degrees. What is the measure of angle $H$ ?

Problem 5 From Unit 4 Lesson 9

The Colorado state flag consists of three horizontal stripes of equal height. The side lengths of the flag are in the ratio $2 : 3$ . The diameter of the gold-colored disk is equal to the height of the center stripe. What percentage of the flag is gold?