Lesson 17
Applying Volume and Surface Area
Let's explore things that are proportional to volume or surface area.
Problem 1
A landscape architect is designing a pool that has this top view:
![An irregular pentagon. Horizontal line, 9 feet. From the right end, slant down and right, 10 point 7 feet, down 1 point 5 feet, left 11 feet, up 12 feet to reach left end of original line.](https://cms-im.s3.amazonaws.com/fZzZQTW1RZssCXkJQAWL7Nsj?response-content-disposition=inline%3B%20filename%3D%227-7.7.newPP.trapezoidpooltop.png%22%3B%20filename%2A%3DUTF-8%27%277-7.7.newPP.trapezoidpooltop.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T163116Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b48885bed1482fa46ca10e5f67e7efe2a96f79aefe24f5bd4606ee9633453ebb)
- How much water will be needed to fill this pool 4 feet deep?
- Before filling up the pool, it gets lined with a plastic liner. How much liner is needed for this pool?
- Here are the prices for different amounts of plastic liner. How much will all the plastic liner for the pool cost?
plastic liner (ft2) cost ($) 25 3.75 50 7.50 75 11.25
Problem 2
Shade in a base of the trapezoidal prism. (The base is not the same as the bottom.)
- Find the area of the base you shaded.
- Find the volume of this trapezoidal prism.
![A prism, height 12. Each base is a trapezoid, parallel sides 8 and 5, non-parallel sides 4 and 5. The side with length 4 is perpendicular to the parallel sides.](https://cms-im.s3.amazonaws.com/TjazBvyzv8hQkgDiFHg2t3W2?response-content-disposition=inline%3B%20filename%3D%227.7.newPP.trapprism.02.png%22%3B%20filename%2A%3DUTF-8%27%277.7.newPP.trapprism.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T163116Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=36a3af276e890a4a2d889ce46dc2057d1f642d531d25c849d859cc304e299980)
Problem 3
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, sides 3 point 1 centimeters, 2 point 6 centimeters, 4 centimeters. The short side is opposite 40 degree angle, middle side, 50 degree angle, longest side, 90 degree angle.](https://cms-im.s3.amazonaws.com/DkfakTmXGvmqw4avYpiP1AAs?response-content-disposition=inline%3B%20filename%3D%227-7.6.B.PP.Image.03.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.B.PP.Image.03.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T163116Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e17005add21e9cf0a14c3b69a6a9b711505d8f469a63cc995f2c204f7a3fd977)