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CONTENT:

(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 $$= \frac{θ}{360^o} × πl^2$$

Also, $$= \frac{θ}{360^o} × 2πl = 2πr \\ \frac{θ}{360^o} = \frac{r}{l}$$

Total surface area of cone $$= πrl = πr^2 \\ πr (l + r)$$

Example 1: Calculate in terms of π, the total surface area of a cone of base diameter 12cm and height 10cm.

Lesson tags: General Mathematics Lesson Notes, General Mathematics Objective Questions, SS1 General Mathematics, SS1 General Mathematics Evaluation Questions, SS1 General Mathematics Evaluation Questions Third Term, SS1 General Mathematics Objective Questions, SS1 General Mathematics Objective Questions Third Term, SS1 General Mathematics Third Term
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