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Curved Surface Area of a Cone is 308 Cm2 and Its Slant Height is 14 Cm. Find the Radius of the Base and Total Surface Area of the Cone. - CBSE Class 9 - Mathematics

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Question

Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find the radius of the base and total surface area of the cone. 

Solution

(1) Given that, 

Slant height of cone= 14cm  

Let radius of circular end of cone=r 

Curved surface area of cone=`pirh` 

`308cm^2=(22/7xxrxx14)cm`        [∵` CSA=308 cm^2`] 

⇒ `r= 308/44cm=7cm` 

Thus, radius of circular end of cone= 7cm 

(ii) Given that CSA= `308cm^2` 

WKT, total surface area of cone 

=curved surface area of cone + area of base 

= `pirl+pir^2` 

=`[308+22/7(7)^2]cm^2` 

= `308+154cm^2` 

= `462cm^2` 

Thus, the total SA of the cone is `462 cm^2` 

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APPEARS IN

 RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 20: Surface Areas and Volume of A Right Circular Cone
Ex.20.10 | Q: 15 | Page no. 8
Solution Curved Surface Area of a Cone is 308 Cm2 and Its Slant Height is 14 Cm. Find the Radius of the Base and Total Surface Area of the Cone. Concept: Surface Area of a Right Circular Cone.
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