SS1 Third Term Mathematics Lesson Note – Mensuration II

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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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