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Contents
Area of Sector & Length of Arc
Surface Area of Cones & Pyramids
Volume of Sphere
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Volume of Sphere If we fill the cylinder with water and then remove the sphere from the cylinder, the water will only take up ⅓ of the cylinder. Thus, the volume of the sphere is ⅔ the volume of the cylinder having the same diameter as the sphere and height equal to the diameter. Vol. of cylinder = pr2h
= pr2(2r)
= 2 pr3
Vol. of
sphere = ⅔ x 2pr3
= 4/3 pr3
Example 1
Vol.
= ½ x 4/3 pr3
= ⅔ x p x 0.14 x
0.14 x 0.14
= 0.006m2
Example
2
Seven
steel balls, each of diameter 4cm, are dropped into a tall cylinder flask of
radius 5cm, which contains water. By how much does the water level rise?
(Assume the balls are entirely submerged.)The
ball displace an equal volume of water, so it will rise d cm.Vol.
of 7 balls
 Increase
in vol. of water = pr2d
= p x 5 x 5 x d
= p x 25 x d
Hence
 = p
x 25 x dd
= (7 x 4 x 8)/(3 x 25)
= 2.99 cm (3 s.f.)
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