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Solve Real-World Volume Problems

Students apply volume formulas to solve real-world problems involving rectangular prisms and composite figures. Problems require students to interpret context, choose appropriate strategies, and verify the reasonableness of answers.

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Solve Real-World Volume Problems

Grade 5 · Volume Formulas and Applications · question 1 of 3

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20 rungs. A star at the top.

A shipping crate holds 36 cubic feet. Its floor is 3 feet by 3 feet. How tall is the crate?

How it is taught

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Volume is the space inside a box.

For a rectangular prism, multiply the three edges.

Read it: Volume = length × width × height

A box 4 by 2 by 3 holds 4 × 2 = 8 cubes in its bottom layer, and 3 layers: 8 × 3 = 24. So V = l × w × h = 24 cubic units, and V = B × h: the base's area times the height.

  1. Find the base: length × width, 4 × 2 = 8 square units.
  2. Multiply by the height, which counts the layers: 8 × 3 = 24.
  3. For a solid made of two boxes, find each box's volume, then add them.

The base's area is the number of cubes in one layer.

The height is the number of layers, so base × height counts every cube.

Two boxes that do not overlap each fill their own space, so their volumes add.

V = l × w × h = B × h, in cubic units.

Adding the edges, 4 + 2 + 3, instead of multiplying them.

Volume multiplies: 4 × 2 = 8, then 8 × 3 = 24 cubic units.

Kofi builds a wooden planter in the orchard. It is a box 5 by 2 by 2 feet. What is its volume in cubic feet? — 20. 5 × 2 = 10, and 10 × 2 = 20 cubic feet.

Fish tank: 12 in × 8 in × 10 in

Maya is filling this fish tank. It's twelve inches long, eight inches wide, and ten inches tall. How much water will it hold?

Grade 5 · Finding the volume of a fish tank

A fish tank is a rectangular prism, so we can use the volume formula.

Volume equals length times width times height.

The length is twelve inches.

The width is eight inches.

The height is ten inches.

First, multiply twelve times eight. That's ninety-six.

Now multiply ninety-six times ten. That's nine hundred sixty.

Let's check: about ten times eight times ten is eight hundred. Nine hundred sixty is close, so our answer is reasonable.

Volume is measured in cubic units, so the answer is nine hundred sixty cubic inches.

Maya's fish tank holds nine hundred sixty cubic inches of water. Great job!

Now you try. Find how much this tank holds. What is the volume?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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