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Chapter 3: Q 62. (page 301)

Prove that the lateral surface area of a right circular cone

is equal to 蟺谤濒, where r is the radius of the cone and

l is the length of the diagonal of the cone, that is, the

distance from the vertex of the cone to a point on its

circumference.

Short Answer

Expert verified

Hence it is proved that the lateral surface area of a cone is蟺rlsquare units.

Step by step solution

01

Step 1. Given Information

A cone's surface area is equal to 蟺谤濒, where ris the cone's radius and lis its slant height.

02

Step 2.  Show that the lateral surface area of a right circular coneis equal toπrl

Let's consider,

r is the radius of the cone.

lis the slant height.

The circumference of the base is 2蟺谤

Length of arcABis 2蟺谤

Area of sectorOABArea of circle with centre atC=Arc lengthABof sectorOABCircumference of circle with centre atO

鈭�Area of sectorOAB蟺l2=2蟺r2蟺l=rl

So, Area of sector OAB,

A=rl脳蟺l2=蟺rl

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