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Find the area of canvas required for a conical tent of height 24 m and base radius 7 m. - Mathematics

Answer in Brief

Find the area of canvas required for a conical tent of height 24 m and base radius 7 m.

 
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Solution

The amount of canvas required to make a cone would be equal to the curved surface area of the cone.

The formula of the curved surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as 

Curved Surface Area = `pirl`

It is given that the vertical height ‘h’ = 24 m and base radius ‘r’ = 7 m.

To find the slant height ‘l’ we use the following relation

Slant height,  l = `sqrt(r^2 + h^2)`

= ` sqrt(7^2 + 24^2)`

= `sqrt(49+576)`

= `sqrt(625)`

l = 25

Hence the slant height of the given cone is 25 m.

Now, substituting the values of r = 7 m and slant height l = 25 m and using ` pi 22/7` in the formula of C.S.A,

We get 

Curved Surface Area = `((22).(7)(25))/7`

= (22) (25)

= 550 

Therefore the Curved Surface Area of the cone is 550 m

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 20 Surface Areas and Volume of A Right Circular Cone
Q 6 | Page 24
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