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Contents
Area of Sector & Length of Arc
Volume of Cones & Pyramids
Surface Area of Cones & Pyramids
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Volume of Cones & Pyramids The volume, V of a pyramid or a cone with base area A and height h is given by V= ⅓Ah
Example 1
(a) height 20cm and a rectangle base 8cm by 6cm;
(b) height 9cm and a triangular base with sides 7cm and 8cm at right angles to each other.
(a) V=
⅓Ah
= ⅓ x 8 x 6 x 20
= 320cm3
(b)
V = ⅓Ah
= ⅓
(½ x 7 x 8) x 9
= 84cm3
Example
2
A
cone has a circular base of radius 14cm, a height of 48cm and a slant height
of 50cm. Calculate the volume of the cone. (Take p
to be 22/7)V
= ⅓pr2h
= ⅓
x 22/7 x 14 x 14 x 48
= 9 856 cm3
Example
3
The
following shows two types of containers each 15cm deep. One is a rectangle
pyramid and the other is a cone. Determine which container holds more water
when full, and by how much?Vol.
of pyramid = ⅓
x 4 x 7 x 15
= 140cm3
Vol. of cone = ⅓
x 3 x 3 x 15 x p
= 45p cm3
Difference = 45p cm3 - 140cm3 = 1.37cm3 (3
s.f.)
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