1. A cooling system can decrease the temperature of 60 cubic feet of air by 10°F in 1 minute. The attic of a particular townhouse is shown in the diagram below.

How many minutes will it take for the cooling system to decrease the temperature of the entire attic by 10°F?


A. 40 minutes

Correct!  You found the area of the triangular base then multiplied by 20 feet to find the volume. The last step was to divide the volume by the rate of 60 cubic feet per minute. 

B. 80 minutes

Incorrect. Remember to find the volume of a TRIANGULAR prism.

C. 120 minutes

Incorrect. Remember to multiply the area of the base by 20 to find the volume of the prism, and then divide by 60 to find the number of minutes required for cooling.

D. 320 minutes

Incorrect. The base of a triangular prism is a triangle. Use the formula chart to help you determine the volume of a triangular prism, and then divide that volume by the amount of air that can be cooled in 1 minute.

 

  1. Boxes of candy in the shape of a rectangular prism measuring 6 inches by 6 inches by 2 inches are packaged for Christmas delivery in larger shipping boxes. The shipping boxes are also rectangular prisms that measure 18 inches by 18 inches by 8 inches.

How many candy boxes can be packed in each shipping box?

A. 36 candy boxes

Correct! 9 candy boxes will fit in each layer inside the shipping box, and there will be 4 layers of candy boxes inside the shipping box.

B. 12 candy boxes

Incorrect. This is only one column of candy boxes within the shipping box. How many columns of candy boxes will be contained inside the shipping box? Use that additional information to determine your answer.

C. 4 candy boxes

Incorrect. There will be 4 candy boxes stacked on top of each other inside the shipping box. How many of these stacks will be contained inside the shipping box? Use that additional information to determine your answer.

D. 3 candy boxes

Incorrect. There will be 3 candy boxes side-by-side along the width of the shipping box. How many rows of 3 candy boxes will fit inside the shipping box? Use that additional information to determine your answer.

 

  1. Which of the following methods could be used to determine the volume of the pyramid whose net is shown below?

A. Find the area of one of the triangles and multiply by the height of the pyramid.

Incorrect. This is missing the last step, divide by 3 or multiply by 1/3.

B. Find the area of one triangle and multiply that number by four.

Incorrect. This will find the total surface area of the triangular pyramid.

C. Find the area of one triangle, multiply that number by the height or one triangle, and multiply the result by 1 3

Incorrect. The height of one triangle is the slant height of the triangular pyramid. To determine the volume of a pyramid, you will need to use the height of the pyramid.

D. Find the area of the central triangle and multiply by the height of the pyramid. Then multiply the result by 1 3 .

Correct. This is the net of a triangular pyramid. The formula for volume of a pyramid is V = 1/3 Bh.

 

  1. The hopper of a grain loader is in the shape of an inverted square pyramid. It can load grain into a railcar through an opening in the bottom of the hopper at an average rate of 48 cubic feet per minute.

Find the time required to empty the full hopper into a railcar.

A. 8 minutes

Correct! The Volume of the square pyramid (the hopper) was found, divided by 48 cubic feet per minute to find the number of minutes it would take to empty the hopper.

B. 384 minutes

Incorrect. After finding the volume of the hopper, divide by 48 cubic feet per minute to find the number of minutes required to empty the hopper.

C. 2 minutes

Incorrect. Remember the volume formula is the area of the square base multiplied by the height then multiply by 1/3. After the volume is found divide it by 48 cubic feet per minute to find the time needed to empty the hopper.

D. 24 minutes

Incorrect. Remember when finding the volume to either divide 3 or multiply by 1/3.