Skip to content
Brainsladder

Find Volume of 3D Figures

Students solve real-world and mathematical problems involving volume of prisms and other 3D figures. They apply V = Bh (where B is the base area) to right prisms with triangular and other polygonal bases, and solve problems involving composite solids.

Try three of them

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

Find Volume of 3D Figures

Grade 7 · Geometry · question 1 of 3

0 of 20

20 rungs. A star at the top.

4 cm4 cm6 cm

The triangular box is a triangular prism. What is its volume?

Read the triangle and the length.

How it is taught

0:00 of 3:49

Volume of a prism is base area times height.

If volume and base area are known, divide to find height.

Read it: Volume of a triangular prism

This prism's end is a triangle with base 8 and height 3, and the prism is 5 long. The triangle is half of an 8 by 3 rectangle: 8 × 3 = 24, so the end is 12. Each slice 1 unit thick holds 12 cubic units, and there are 5 slices: 12 × 5 = 60 cubic units.

  1. Find the area of the triangular end: 1/2 × base × height.
  2. Multiply the end's area by the prism's length.
  3. Write the volume in cubic units.

A triangle is half of the rectangle around it, so its area is half of base × height.

Every slice 1 unit thick is the same triangle, so it holds the end's area in cubic units.

The length counts the slices, so the volume is the end's area times the length, just as a box's is its base times its height.

Volume of a prism = the area of its end × its length.

Forgetting the half: 8 × 3 × 5 = 120.

The end is half its rectangle: 1/2 × 8 × 3 = 12, and 12 × 5 = 60.

A triangular prism is 9 units long. Its end is a triangle with base 7 and height 8. Its volume is ___ cubic units. — 252. The end is 1/2 × 7 × 8 = 28, and 28 × 9 = 252.

Triangular prism: V = B·h with B = 12, h = 10

Picture a camping tent shaped like a triangular prism. How much air does it hold inside?

Look at this tent. It has a triangle face that's six feet wide and four feet tall, and the tent runs ten feet long.

Grade 7 · Volume of a triangular prism using V = Bh

For ANY prism, the volume equals the area of the base times the height: V equals B times h.

The base of a prism is the shape on the end — here, the triangle. Let's find its area first. That's our B.

A triangle's area is one-half times its base times its height.

One-half times six times four equals twelve. So B is twelve square feet.

Now multiply that base area by how far the prism stretches back — the ten feet of length.

Twelve times ten equals one hundred twenty.

The tent holds one hundred twenty cubic feet of air. For any prism: V equals B times h. Nice work!

Now you try. Count the flat faces on this solid. How many flat faces?

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