Lesson · Grade 7 · Mathematics
Volume Is the Area of the Base Times the Height
- Grade 7
- Mathematics
- 1 min 10 s
- British Columbia
- BC7-MA-52
A 5 cm by 3 cm by 4 cm box is filled with 1 cm cubes: its base area is 5 × 3 = 15 cm², so one layer holds 15 cubes, and 4 layers stack up to give 15 × 4 = 60 cm³. A cylinder then fills up the same way with layers the shape of its circle base, and the video ends on the rule: volume = area of the base × height.
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In one sentence
The question this lesson answers
How much space is inside this box, which is a rectangular prism?
The bottom face is the base, 5 centimetres long and 3 centimetres wide.
Transcript
What the lesson says
How much space is inside this box, which is a rectangular prism?
The bottom face is the base, 5 centimetres long and 3 centimetres wide.
The area of the base is 5 times 3, which is 15 square centimetres.
Volume is counted in cubes 1 centimetre on every side, called cubic centimetres.
One layer of 15 cubes covers the base, one cube for each square centimetre.
The box is 4 centimetres tall, so 4 layers stack up inside.
4 layers of 15 cubes make 15 times 4, which is 60 cubes.
So the volume of the box is 60 cubic centimetres.
That means volume is the area of the base times the height.
A cylinder works the same way, but its base is a circle.
Every layer matches the circle base, so multiply the area of the circle by the height.
Remember: volume is the area of the base times the height.
Curriculum
Where this fits
- British Columbia, Grade 7
Mathematics, Geometry and measurement: volume of rectangular prisms and cylindersBC7-MA-52
Previous: Area of a Circle from the Radius or the DiameterNext: Volume of a Rectangular Prism
- British Columbia, Grade 8
Mathematics, Geometry and measurement: surface area and volume of regular solids, including triangular and other right prisms and cylindersBC8-MA-27
Previous: Surface area of a cylinder: two circles and a rectangleNext: Volume of a Triangular Prism
This lesson is also listed in Grade 8.
The outcomes and strands follow the British Columbia curriculum.
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