Lesson · Grade 8 · Mathematics
Surface area of a cylinder: two circles and a rectangle
- Grade 8
- Mathematics
- 1 min 46 s
- British Columbia
- BC8-MA-26
A can with radius 4 cm and height 10 cm is taken apart: its top and bottom become two equal circles, and its label unrolls into a rectangle 10 cm tall and as long as the circumference, 2 × π × 4 cm. Using the calculator's π key, the two circles come to about 100.53 cm² and the rectangle to about 251.33 cm², giving 351.86, or about 351.9 cm², with warnings to use the radius rather than the diameter and to count both circles.
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In one sentence
The question this lesson answers
This can is a cylinder. What is its surface area: the total area of all its surfaces?
The radius goes from the centre of a circle to its edge: here, 4 centimetres. The height is 10 centimetres.
Transcript
What the lesson says
This can is a cylinder. What is its surface area: the total area of all its surfaces?
The radius goes from the centre of a circle to its edge: here, 4 centimetres. The height is 10 centimetres.
Take the can apart. The top and the bottom are two equal circles.
Peel off the label: it unrolls into a rectangle as tall as the can, 10 centimetres.
Its length wraps once around the can: the circumference, the distance around a circle.
The circumference is 2 times pi times the radius: here, 2 times pi times 4 centimetres.
One circle's area is pi times r squared. Use the pi key on a calculator.
For two circles: 2 times pi times 4 squared, which is 2 times pi times 16, about 100.53 square centimetres.
The rectangle is length times height: 2 times pi times 4, times 10, about 251.33 square centimetres.
Add the parts: 100.53 plus 251.33 is 351.86, about 351.9 square centimetres.
Careful: the diameter is 8 centimetres, but the radius is half of it: 4 centimetres.
And count both circles: the top and the bottom.
Surface area of a cylinder: two circles plus a rectangle as long as the circumference.
Curriculum
Where this fits
- British Columbia, Grade 8
Mathematics, Geometry and measurement: surface area and volume of regular solids, including triangular and other right prisms and cylindersBC8-MA-26
Previous: Surface Area of a Triangular PrismNext: Volume Is the Area of the Base Times the Height
The outcomes and strands follow the British Columbia curriculum.
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