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WEEK 5
TOPIC: MENSURATION
CONTENTS:
(e) Relation between the sector of a circle and the surface area of a cone.
(f) Surface area and volume of solids; (i) Cube, cuboids (ii) Cylinder (iii) Cone (iv) Prisms (v) Pyramids.
Relation between the sector of a circle and the surface area of a cone.
If a sector of a circle AOB is cut and folded into a come as shown in the diagram below.
The arc AB becomes the circumference of the base of the cone. The radius R becomes the slant edge l of the cone.
∴ Arc AB = 2πr
From the above diagram.
The area of the sector = area of the curved surface of the cone
Length of arc AB = circumference of the circular base of the cone
Curved surface area of cone = θ/3600 x πl2
Also, θ/3600 x 2πl = 2πr
θ/3600 = r/l
Total surface area of cone = πrl + πr2
= πr(l + r).
Example 1: Calculate in terms of π, the total surface area of a cone of base diameter 12cm and height 10cm.
Solution
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