Math with Measurements – Volume I

Volume refers to the space taken up by an object itself, while capacity refers to the amount of a liquid or other pourable substance a container can (or does) hold.Here is an example: This jug has a capacity of 250ml.The volumeof milk in the jug is 175ml.Thevolumeof milk needed to fillthe jug is 250ml.

The volume is how much milk is in the jug. It is measured in cubic units (3D -three-dimensional). Remember that length is one-dimensional (1D) and area is two-dimensional (2D - square units).

The volume of a rectangular solid can be found using cubes. For example: take a box and fill the bottom of one of the boxes with the cubic inches (or cubic centimeters).

This box can hold 4rows of cubes with 5cubes in each row,(connect this with thearea of the base being20 square units).

Next, take the cubic inches and pile them up until the box’s height is taken into consideration and filled to the top.

For example: This box can hold 3 layers of 20 cubes in each layer, which would result in a volume of 60 cubic units (whether cubic inches, cubic centimeters, etc.)

Hence, if we know the number of cubes that will cover the bottom of the box (the area of the base), and if we know how many layers will fit in the box (the number of layers or the height), then the number of cubes the box will hold (its volume) can be determined.

Prisms are 3-dimensional figureswith the following characteristics:

  1. Prisms have two bases (shaded in the pictures on the next page) that are polygons.
  2. The bases are translation images of each other in space. So, the bases are congruent and lie in parallel planes.

Calculating volume of 3-D figures – prism or cylinder – using the following:

Volume of Prisms = (area of base) × (height)

Use the given figure to find its volume in cubic units.

4×4×4 - 3×2×2 = 5254

  1. The volume of the rectangular box is 200 cm3. What is the value of x?

Answer: 10 (200 ÷5÷4)

  1. Determine the volume of the triangular prism (units in cm).

½ × 8 × 15 × 24 = 1440 cm3

  1. A 12-ounce aluminum soft drink can is about 12 centimeters high. It has a radius of about 3.2 centimeters. What is its volume?

π × (3.22) × 12 ≈386.04 cm3.

  1. In Figure 1 a cylinder with a diameter of 12 centimeters is filled with water to a height of 8 centimeters. In Figure 2 a rock is submerged in the cylinder. Which of the following is closest to the volume of the rock?
  1. 139 cm3
  2. 418 cm3
  3. 1674 cm3
  4. 1323 cm3
  1. A company is considering packaging a new product in either a cylinder or a rectangular prism container. For packaging purposes, the height of the container must be 12 centimeters. The cylinder being considered has a base with diameter 10 centimeters. The rectangular prism being considered has a square base. Find the length of the side of the base of the rectangular prism that will hold approximately the same amount as the cylinder container. Round your answer to the nearest hundredth.

Cylinder: π × (52) × 12 ≈ 942.48 cm3

Prism: (S2) × 12 = 942.48S = 8.86

  1. A locomotive on a freight train is pulling cars of coal. If there are 80 full cars to pull, how many times as heavy is the load as it would be if there were 40 full cars to pull?

2 times

  1. You have two similar cubes made of the same plastic. The edges of one cube are 1 cm long, and the edges of the other are 1 in. long. Remember that 1 in. = 2.54 cm.

a. What is the ratio of the surface area of the centimeter cubeto the surface area of the inch cube?

(2.54)2:1 = 6.45:1

b. What is the ratio of the volume of the centimeter cube to thevolume of the inch cube?

(2.54)3:1 = 16.39:1

  1. Ryan is packing books into a rectangular box. All the books are the same size.

What is the largest number of books that will fit inside the box?

Answer: 12

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