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Lesson · Grade 10 · Workplace Mathematics

Rearranging a volume formula to find a missing height

  • Grade 10
  • Workplace Mathematics
  • 2 min 19 s
  • British Columbia
  • BC10-MA-55

A can must hold 1000 cm³ with a radius of 5 cm, so the video rearranges V = πr²h to h = V ÷ πr² before putting in any numbers, then works out h = 1000 ÷ 78.54 ≈ 12.7 cm and checks it by putting the height back into the formula. It warns against dividing by 2r or πr, which are lengths and not areas, then uses the same idea on a 1.2 m³ box with a 1.5 m by 0.8 m base (height 1 m) and ends on the recap: height = volume ÷ base area.

Concept: Rearranging a volume formula to find a missing measurement

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In one sentence

The question this lesson answers

A can must hold 1000 cubic centimetres, or 1 litre, with a radius of 5 centimetres. How tall must it be?

Volume is the amount of space inside a solid. For a cylinder, V equals pi r squared h.

Transcript

What the lesson says

A can must hold 1000 cubic centimetres, or 1 litre, with a radius of 5 centimetres. How tall must it be?

Volume is the amount of space inside a solid. For a cylinder, V equals pi r squared h.

r is the radius, from the centre of the circle to its edge, and h is the height.

Pi r squared is the area of the circle at the bottom, called the base area.

Before putting in numbers, rearrange the formula to get h on its own. This is called making h the subject.

h is multiplied by pi r squared, so divide both sides by pi r squared.

On the right, pi r squared cancels, leaving h equals V divided by pi r squared.

Now the numbers. The base area is pi times 5 squared, about 78.54 square centimetres.

So h equals 1000 divided by 78.54, which is about 12.73.

To one decimal place, the can must be about 12.7 centimetres tall.

Check by putting 12.73 back in: pi times 5 squared times 12.73 is about 1000 cubic centimetres.

A common mistake is to divide by 2r or pi r. Those are lengths, not areas. The base area is pi r squared.

The same idea works for a box holding 1.2 cubic metres, on a base 1.5 metres by 0.8 metres.

Its base area is 1.5 times 0.8, which is 1.2 square metres.

So the height is 1.2 divided by 1.2, which is 1 metre. Check: 1.5 times 0.8 times 1 is 1.2.

For a cylinder or a box, rearrange first: height equals volume divided by base area.

Curriculum

Where this fits

British Columbia, Grade 10

Workplace Mathematics 10, Geometry and measurement: surface area and volumeBC10-MA-55

Previous: Converting between metric and imperial lengthsNext: Surface Area or Volume? What the Job Needs

The outcomes and strands follow the British Columbia curriculum.

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