Lesson · Grade 7 · Mathematics
Volume of a Cylinder: Base Area Times Height
- Grade 7
- Mathematics
- 1 min 15 s
- British Columbia
- BC7-MA-54
A can with a radius of 5 cm and a height of 10 cm is shown as 10 circle layers stacked on its base, which shows why its volume is the area of the base times the height. The base area is worked out as π × 5 × 5 ≈ 3.14 × 25 = 78.5 cm², then multiplied by the 10 cm height to get about 785 cm³, ending on the recap Volume = π × r × r × h.
Concept: Volume of a cylinder
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In one sentence
The question this lesson answers
How much space is inside this can, which is a cylinder?
Its radius is 5 centimetres, and it is 10 centimetres tall.
Transcript
What the lesson says
How much space is inside this can, which is a cylinder?
Its radius is 5 centimetres, and it is 10 centimetres tall.
The bottom of a cylinder is a circle, called the base.
Think of the can as 10 layers, each a copy of the base, 1 centimetre thick.
So the volume is the area of the base times the height.
The base is a circle, so its area is pi times r times r.
The radius is 5, so put 5 in place of each r.
Pi is about 3.14, and 5 times 5 is 25.
3.14 times 25 is 78.5, so the base area is about 78.5 square centimetres.
Now multiply the base area by the height, 10 centimetres.
78.5 times 10 is 785.
So the can holds about 785 cubic centimetres.
Remember: the volume of a cylinder is pi times r times r times the height.
Curriculum
Where this fits
- British Columbia, Grade 7
Mathematics, Geometry and measurement: volume of rectangular prisms and cylindersBC7-MA-54
Previous: Volume of a Rectangular PrismNext: The Four Quadrants
- British Columbia, Grade 8
Mathematics, Geometry and measurement: surface area and volume of regular solids, including triangular and other right prisms and cylindersBC8-MA-29
Previous: Volume of a Triangular PrismNext: The Pythagorean Theorem: Squares on the Sides of a Right Triangle
This lesson is also listed in Grade 8.
The outcomes and strands follow the British Columbia curriculum.
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