1. Lesson 2

1.6. Explore 2

Mathematics 20-3 Module 7

Module 7: Volume and Capacity

 

The next example shows how this same formula is used for a cylinder in a capacity situation.

 

Example

 

This is a photo of a steel drum located near a well.

iStockphoto/Thinkstock

A cylindrical steel drum has a diameter of 22.5 in and a height of 33.5 in. If 1 gal = 277.42 in3, what is the capacity of the drum in gallons? Round to one decimal place.

 

Solution

 

The steel drum is cylindrical. The diameter is 22.5 in. Therefore, the drum radius is 11.25 in.

 

 

 

The formula for capacity of a cylinder is V = B × h. B is the area of the circular base, . So,

 

 

 

Substitute in the known values for r and h.

 

 

 

Convert cubic inches to gallons.

 

 

 

There are approximately 48.0 gal in the steel drum.


formula sheet

You may now want to add the volume and capacity formula for prisms and cylinders to the Formula Sheet.

 

Self-Check 1
  1. Open Prisms and Cylinders - Activity A. Complete the five assessment questions at the bottom of the gizmo.

    This is a play button that opens Prisms and Cylinders - Activity A.
    Screenshot reprinted with permission of ExploreLearning.
  2. What is the volume of wood in a -in standard sheet of plywood? A sheet of plywood is 8 ft × 4 ft. hint Answer

    This photo is of a stack of plywood on a cart in a store’s lumber department.
    iStockphoto/Thinkstock
  3. Convert the volume of wood in the -in sheet of plywood from question 2 into cubic inches. Answer

  4. A wooden feed trough with trapezoidal ends has inside dimensions as shown in the following graphic.

    This is a graphic of a feed trough. The trough is 8 ft long, 12 in deep, and measures 10 in wide at the base and 18 in wide at the top.

    1. Determine, to the nearest cubic foot, the maximum amount of feed the trough can hold. Answer

    2. What is the capacity, to two decimal places, of this trough in US gallons? Answer


textbook
  1. Answer question 3 from “Build Your Skills” on page 145 of MathWorks 11. Answer


1ft3 = 7.48 gal (US)
All dimensions must be in the same units.