Grade 9
Surface Area and
Volume
Given the square blocks above, can you say how many blocks there are? ______________
If the blocks have the following measurements,
 What is the area of the exposed surfaces of the blocks? __________
How would we go about working out the volume of the stacked blocks? __________________
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1. Volume
Volume is the amount of space that an object occupies.
In general, any right prism or cylinder can be found using the following formula:
Volume = area of base x height
Therefore,
Remember: Area has the
units2, so volume must now
have units3!
Volume of a rectangular right prism:
Volume = area of base x height
Volume = l x b x h
Volume of a cylinder:
Volume = area of base x height
Volume = r 2 h
Volume of triangular right prism:
Volume = area of base x height
Volume =
1
axbxh
2
Example:
Find the volumes of the rectangular prism and cylinder below:
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Remember the following conversions:
Finding the height and radius given the volume:
Example:
a) Given a cylinder with radius 25cm and volume 400l,
calculate the height of the cylinder (to the nearest cm).
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b) Given the cylinder with height 300 cm and volume 45000 l,
calculate the radius of cylinder (to the nearest cm).
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1000 cm3 = 1000 ml = 1 l
1000 l = 1 kl = 1m3
Volume of irregular prisms:
Example:
Find the volume of the prism alongside:
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Hint: Calculate the volume of the
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prisms below and subtract them:
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2. Surface Area
Calculating the surface area of a cylinder and a right prism:
Examples:
a) Cylinder:
Draw a net:
Total surface area of a cylinder = 2(area of the base) + (perimeter of base x height)
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b) Rectangular prism:
Draw a net:
Total surface area of a rectangle prism = 2(area of the base) + (perimeter of base x height)
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c) Triangular prism:
Draw a net:
By Pythagoras: _____________________________
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Total surface area of a triangular prism = 2(area of the base) + (perimeter of base x height)
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