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Apply the Volume Formula V = B × h

Students use the formula V = B × h, where B is the area of the base, to find the volume of right rectangular prisms. They calculate the area of the base first, then multiply by the height, connecting area and volume concepts.

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Apply the Volume Formula V = B × h

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

0 of 20

20 rungs. A star at the top.

5 ft4 ft3 ft

The shipping box starts with its base. Then multiply by height.

Read the edges.

How it is taught

0:00 of 3:18

Volume is the base area times the height.

B is the area of the base, not one edge.

6 in3 in3 in

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.

A box is 7 by 4 by 2. Its volume is ___ cubic units. — 56. The base is 7 × 4 = 28, and 2 layers: 28 × 2 = 56.

V = (4 × 3) × 5

How much space fits inside this box? That's what volume measures.

Grade 5 · Find the volume of a rectangular prism

Our box is four units long, three units deep, and five units tall.

To find the volume, we use the formula: V equals B times h.

B is the area of the base — the bottom face of the box.

The base is a four-by-three rectangle, so we multiply four times three.

Four times three is twelve. So B equals twelve square units.

h is the height — and our box is five units tall.

Now we put it together: V equals twelve times five.

Twelve times five is sixty.

The volume is sixty cubic units. Nice work!

Now you try. Use the base and the height to find the volume. How much space inside?

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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