## Monday, February 14, 2011

### Patrick's Math Notes Post

VOLUME

BASE (of a prism of cylinder)
-Any face of a prism that shows the named shape of the prism.
-The base of a rectangular prism is any face.
-The base of a triangular prism a triangular face.
-The base of a cylinder is a circular face.

HEIGHT (of a prism or cylinder)
-The perpendicular distance between the two bases of a prism or cylinder.

VOLUME
-The amount of space an object occupies
-Measured in cubic units

ORIENTATION
-The different position of an object formed by translating, rotating or reflecting the object.

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Volume of a Rectangular Prism.

area of base X height
l x w
6 x 5 = 30cm²

30cm² x 10 cm = 300 cm³

Volume of a Triangular Prism.

area of base X height

b x h /2
7 x 5 / 2 = 17.5 cm²

17.5cm² x 10 cm = 175cm³

Volume of a Cylinder

area of base X height
π X r X r
3.14 X 5 X 5 = 78.5 cm
²

78.5cm² X 10 cm = 785 cm³
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These three videos should help you how to find the volume of a shape.

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Cylinder Volume and Volume Problems

r = d/2
r = 0.26 m/2
r = 0.13 m^2

V = (π x r x r) x h
V = (3.14 x 0.13^2) x 2.4m
V = (0.05m^2) x 2.4 m
V = 0.12m^3

0.12m^3 x 35 = 4.2, (round up) = 5m^3

The volume of concrete required is 5m^3.

a)Volume with the missing piece = l x w x h
Volume with the missing piece = 10cm x 16cm x 10cm
Volume with the missing piece = 1600cm^3

Volume of missing piece = l x w x h
Volume of missing piece = 10cm x 6cm x 5cm
Volume of missing piece = 300cm^3

Volume = 1600cm^3 - 300cm^3
Volume = 1300cm^3

The volume is 1300cm^3

b) You can check your answer by dividing the shape into separate rectangular prisms.