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This page shows questions in the Geometry Modeling public release module at MSDE. Geometry
"Geometry Modeling"

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This is a test question that allows you to enter extended text in your response.

In the right triangle shown, Trish wants to estimate the degree measure of theta. She knows that 10 is less than or equal to A, which is less than or equal to 11 and that 5 is less than or equal to B, which is less than or equal to 6.

Right triangle has legs labeled a and b. The angle opposite side b is labeled theta.

Determine the greatest and least estimates of the degree measure of theta. Explain how you determined each estimate.

Enter your answers and your explanations in the space provided.

Copyright 2023, New Meridian Corporation. Reprinted with permission. All rights reserved. The printing, copying, redistribution, or retransmission of this content without express written permission is prohibited.

This is a question with 2 parts, including a test question that allows you to enter extended text in your response.

Part A

The Pisces Place is a company that makes fish tanks. Corey has sent the company a special order for a fish tank that is a rectangular prism with an open top. He provides a sketch with the dimensions as shown.

A diagram shows the net of a rectangular prism, with a horizontal rectangle and a vertical rectangle intersection in the middle. The middle is labeled base. The length of the vertical rectangle is 54 inches, and the width of the horizontal rectangle is 18 inches. The capacity is 100 gallons. The height of the horizontal rectangle above the base is a question mark.

One cubic foot of water is equivalent to 7.48 gallons. If the capacity of the fish tank is 100 gallons, find the maximum possible height for the fish tank. Round your answer to the nearest thousandth of an inch. Show your work.

Enter your answer and your work in the space provided.

Part B

Corey plans to have the completed fish tank sent to his home. A shipping company offers to ship it at a cost of $0.25 per pound.

Corey knows that his fish tank would weigh a total of 1,100 pounds if it were filled to capacity. One cubic foot of water weight 62.4 pounds.

Use this information to calculate the total cost to ship the fish tank when it is empty. Show your work.

Enter your answer and your work in the space provided.

Copyright 2023, New Meridian Corporation. Reprinted with permission. All rights reserved. The printing, copying, redistribution, or retransmission of this content without express written permission is prohibited.