Videos and solutions to help Grade 7 students learn how to solve real-world and mathematical problems involving volume and surface areas of three- dimensional objects.

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Common Core For Grade 7

• Students solve real-world and mathematical problems involving volume and surface areas of three-
dimensional objects composed of cubes and right prisms.

Opening Exercise

What is the surface area and volume of the right rectangular prism?

Example 1: Volume of a Fish Tank

Jay has a small fish tank. It is the same shape and size as the right rectangular prism shown in the Opening Exercise.

a. The box it came in says that it is a gallon tank. Is this claim true? Explain your reasoning. Recall that 1 gal = 231 in

b. The pet store recommends filling the tank to within 1.5 inches of the top. How many gallons of water will the tank hold if it is filled to the recommended level?

c. Jay wants to cover the back, left, and right sides of the tank with a background picture. How many square inches will be covered by the picture?

d. Water in the tank evaporates each day, causing the water level to drop. How many gallons of water have evaporated by the time the water in the tank is four inches deep? Assume the tank was filled to within 1.5 inches of the top to start.

Exercise 1: Fish Tank Designs

Two fish tanks are shown below, one in the shape of a right rectangular prism (R) and one in the shape of a right trapezoidal prism (T).

a. Which tank holds the most water? Let Vol(R) represent the volume of the right rectangular prism and Vol(T) represent the volume of the right trapezoidal prism. Use your answer to fill in the blanks with Vol(R) and Vol(T).

b. Which tank has the most surface area? Let SA(R) represent the surface area of the right rectangular prism and SA(T) represent the surface area of the right trapezoidal prism. Use your answer to fill in the blanks with SA(R) and SA(T).

c. Water evaporates from each aquarium. After the water level has dropped 1/2 inch in each aquarium, how many cubic inches of water are required to fill up each aquarium? Show work to support your answers.

Exercise 2: Design Your Own Fish Tank

Design at least three fish tanks that will hold approximately 10 gallons of water. All of the tanks should be shaped like right prisms. Make at least one tank have a base that is not a rectangle. For each tank, make a sketch, and calculate the volume in gallons to the nearest hundredth.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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