Areas and Volumes

1 Khan Academy Area and Volume

Please review this video series and answer the following questions.

  • How many inches in a foot?
  • How many square inches in a square foot?
  • How many cubic inches in a cubic foot?
  • How many centimeters in a meter?
  • How many square centimeters in a square meter?
  • How many cubic centimeters in a cubic meter?
  • For each of these draw out a picture of the line, square, or cube with dimensions.

2 Volume with Mixed Units Cubic Centimeters

You have a box that is 1 foot by 6 inches by 10 cm.

  • Draw a diagram of the box and label the length of the sides.
  • What is the volume of the box in cubic centimeters?
  • Show the conversion from cubic centimeters to cubic inches.

(Note that 2.54 cm = 1 inch.)

3 Volume with Mixed Units Cubic Meters

A large box measures 250 cm long by 30 inches high by 4 feet wide.

  • Draw a diagram of the box and label the length of the sides.
  • What is the volume of this box in cubic meters?
  • Show the conversion from cubic meters to cubic feet.

4 Area Conceptions

You have 8 square meters (8 m^2) of area. Is area that equal to

    1. The area of a square 8 meters on each side
    1. The area of 8 squares, each 1 meter on each side
    1. Neither of these

5 Estimate the area of your desktop

You will estimate the area of your desktop you are using while only using your body quantities and making the appropriate conversions.

  • Express your answer in your body units (square handwidths or whatever)
  • Express your answer in square meters
  • Include a drawing of your desktop with your measurements

6 Estimate the volume of bathtub

You are asked to estimate the volume of a bathtub while only using your body quantities and by making the appropriate conversions.

  • Express your answer in your body units (cubic forearms or whatever)
  • Express your answer in cubic meters
  • Include a drawing of your desktop with your measurements

7 Volume and Depth

You have a given volume of water (say 2 gallons) and want to know how deep the water will be when you pour that water into a rectangular fish tank. Assume you know the length, width, and height of the fish tank. Brainstorm and write down a strategy about how you will solve this problem. Hint: if no water is spilled, the two volumes are equal.

8 Find depth of fluid given a volume

You are hosting a birthday party and want to know how deep the water will be in a kiddie pool. The kiddie pool 30 centimeters high and 2 meters by 2 meters at the base. This kiddie pool is a rectangular box, not a cylinder.

You only have 1 cubic meter of water to use for filling the pool. How deep will the water be in centimeters?

9 Cylindrical tank volume

You have a water tank that is modeled as a cylinder with a radius of 1.5 meters and a height of 2 meters. How many cubic meters of water does this tank hold? How many gallons of water?

10 Height of water in a tank

You have a cylindrical tank that has a 1.5 meter radius and is 2 meters high. You need to store 10 cubic meters of water in the tank. How deep will the water be?

11 Rain Water Storage Strategy

To conserve water and improve resilience, imagine you’d like to store all the rainwater from your roof over the course of a year and you’d like to estimate the size of tank you need.

  • What quantities would you need to estimate and why?
  • How will you put these quantities together to make an estimate?
  • What tools from this section will you use?

12 Rain Water Storage Estimate

Write up your estimates of the tank sizes needed that answer the following questions. Assume we are collecting water from our roofs at home.

  • How many gallons total will you need to store a year of rain and how did you estimate this?
  • If the tank is 3 meters in diameter, how tall will it need to be?

13 Tank Scaling

We’d like to increase the amount of water we can store in our cylindrical tanks.

13.1 If you buy a tank with twice the diameter (same height) how much larger is the volume?

  1. twice as much volume
  2. four times as much volume
  3. no way to tell

13.2 If you buy a tank that is twice as tall (same diameter) how much larger is the volume?

  1. twice as much volume
  2. four times as much volume
  3. no way to tell

13.3 If you buy a tank that has twice the circumference as the current tank, how much larger is the volume?

  1. twice as much volume
  2. four times as much volume
  3. no way to tell

14 DIY Area and Volume

Devise a quantitative question and answer it using your knowledge of areas and volumes.