Skip to content
Brainsladder

Find Volume of Composite Figures Using Additive Volume

Students recognize that the volume of a figure made up of two or more non-overlapping rectangular prisms can be found by adding the volumes of each part. They decompose complex figures and apply volume formulas to each part.

Try three of them

Real questions from this skill, graded here. No account, and nothing is saved.

Find Volume of Composite Figures Using Additive Volume

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

0 of 20

20 rungs. A star at the top.

2 in5 in2 in2 in4 in2 in

Find the volume of the bottom box of the shape alone, in cubic inches.

Find the volume of the bottom box.

How it is taught

0:00 of 3:40

A composite figure's volume is the sum of its non-overlapping parts.

Split it, find each volume, then add.

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.

Gus makes a wooden bookend with a tall piece standing on a flat base. It is two boxes: one 2 by 6 by 2 inches, and one 2 by 5 by 5 inches. What is its total volume in cubic inches? — 74. 2 × 6 × 2 = 24, and 2 × 5 × 5 = 50: 24 + 50 = 74 cubic inches.

L-shaped figure: 16 + 8 = 24 cubic units

Some shapes are made of two prisms stuck together. We can find the volume by adding the parts.

Here's an L-shaped block. It's two units deep, built from small unit cubes.

Let's split it into two rectangular prisms — Prism A on the bottom and Prism B on top.

Look at Prism A. It is four units long, two units wide, and two units tall.

Grade 5 · Splitting an L-shape into two prisms

Volume of A is four times two times two — that's sixteen cubic units.

Prism B is two units long, two units wide, and two units tall.

Volume of B is two times two times two — that's eight cubic units.

Now add the two volumes together.

Sixteen plus eight equals twenty-four.

The total volume is twenty-four cubic units. Great job adding the parts!

Now you try. Split this solid into boxes and add their volumes. 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.

More of the library

Every skill has a page

Practise this skill free

14 days of every skill, practice packets, Fluency sheets and up to four students. No card.

Start free