Lesson 16

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 7, Lesson 13.)

Problem 3

For each diagram, decide if \(y\) is an increase or a decrease of \(x\). Then determine the percentage that \(x\) increased or decreased to result in \(y\).

Two tape diagrams of equal size. Top diagram, 4 parts, 3 blue, total x, 1 part white. Bottom diagram, solid yellow, y.
Two tape diagrams of equal length.  Top diagram, 5 parts, 3 blue, total x, 2 white. Bottom diagram, solid yellow, y.
Two tape diagrams. Top diagram, 3 parts total x. Bottom diagram the same size as two parts above, solid, y.
Two tape diagrams. Top diagram, 3 parts, total x. Bottom diagram same size as one part above, solid, y.
(From Unit 4, Lesson 9.)

Problem 4

Noah is visiting his aunt in Texas. He wants to buy a belt buckle whose price is $25. He knows that the sales tax in Texas is 6.25%.

  1. How much will the tax be on the belt buckle?
  2. How much will Noah spend for the belt buckle including the tax?
  3. Write an equation that represents the total cost, \(c\), of an item whose price is \(p\).
(From Unit 4, Lesson 10.)