objective: to be able to use the formula for the curved surface area of a cone, alongside other...

Objective: To be able to use the formula for the Curved Surface Area of a Cone, alongside other mathematical topics

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Objective: To be able to use the formula for the Curved Surface Area of a Cone, alongside other mathematical topics

Starter

Calculate the Area and Perimeter of this sector of a circle

6cm

220°

Area of the sector: Perimeter of the sector:

(Add on the 2 radii)

Curved Surface Area of a Cone

• Today we will see how to find the Surface Area of a Cone

• The base of a Cone is a circle which we have already seen how to work out

• The new part is the Curved Surface Area around the top…

Base

Curved Surface Area

Curved Surface Area of a Cone

Area of the sector:

Base Circumference = 2πr

2πr

Circumference of the sector:The circumference of the base of the cone is equal to the arc length on the sector…

(This sector is made by unfolding the curved area

of the cone)

C = 2πr

Divide by 2π

Multiply by 360

Divide by l

Swap the ÷ 360

Replace θ from the previous

equation

Top x Top Bottom x Bottom

Cancel the 360s and an l from top and

bottom

Curved Surface Area of a Cone

Curved Surface Area of a Cone = πrlr = the radius of the base of the

Cone

l = the length of the slope of the

cone

Objective: To be able to use the formula for the Curved Surface Area of a Cone, alongside other mathematical topics

Curved Surface Area of a Cone

• Calculate the Surface Area of this Cone

4cm

10cm

Objective: To be able to use the formula for the Curved Surface Area of a Cone, alongside other mathematical topics

Curved Surface Area of a Cone

• Calculate the Curved Surface Area of this Cone

3cm

6cm

You will need to use Pythagoras’ Theorem to find the slant height…

Objective: To be able to use the formula for the Curved Surface Area of a Cone, alongside other mathematical topics

PlenaryCurved SA of the Cone

Curved SA of the Cylinder

The Base

In Total

Objective: To be able to use the formula for the Curved Surface Area of a Cone, alongside other mathematical topics

Plenary

Page 10: Objective: To be able to use the formula for the Curved Surface Area of a Cone, alongside other mathematical topics

Summary

• We have learnt how to work out the Surface Area of a Cone

• We have seen where the formula comes from

• We have used it alongside other topics we have covered

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