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.
  1. How much water will be needed to fill this pool 4 feet deep?
  2. Before filling up the pool, it gets lined with a plastic liner. How much liner is needed for this pool?
  3. 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.)

  1. Find the area of the base you shaded.
  2. 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.
(From Unit 6, Lesson 15.)

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.


(From Unit 1, Lesson 17.)