Maths

Common mistakes in volume

3 mistakes learners make with volume, each one named and explained.

All common mistakes

Volume is the area of the base times how many layers high it goes, which is why every dimension has to be in the product.

Only two of the three dimensions used

What it looks like

A cuboid's volume is worked out from two of its edges, so the answer is an area.

Why it happens

Area is the calculation practised most, and two numbers is the shape it expects.

A worked example

Question. 4 cm by 3 cm by 10 cm

A common answer. 4 x 3 = 12

The answer. 4 x 3 x 10 = 120

Why. Volume fills a solid, so all three edges have to be used.

Put the two side by side

Two lengths multiplied: cm squared, an area.
Three lengths multiplied: cm cubed, a volume.

Count the numbers you used. A volume always uses three.

Surface area given where volume was wanted

What it looks like

The areas of the six faces are added and offered as the volume.

Why it happens

Both are calculated from the same three edges and both describe the size of the solid.

A worked example

Question. 4 by 3 by 10

A common answer. 2(12 + 40 + 30) = 164

The answer. 120

Why. Surface area is what you would paint; volume is what you could pour in.

Put the two side by side

Surface area: cm squared.
Volume: cm cubed.

The unit decides. Three lengths multiplied gives a cubed unit, every time.

The three dimensions added

What it looks like

Volume is given as the three lengths added together.

Why it happens

Three numbers appear and adding is the operation that needs no decision.

A worked example

Question. 4 cm by 3 cm by 10 cm

A common answer. 4 + 3 + 10 = 17

The answer. 4 x 3 x 10 = 120

Why. Volume counts how many unit cubes fit inside, which is a multiplication.

Put the two side by side

17 is smaller than one of the edges.
120 is how many centimetre cubes fill it.

A volume is always much larger than any one edge. If it is not, something was added.

WAJD spots these patterns in your child's answers and names the one behind their wrong answers, instead of just marking them wrong.

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