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The Radius of the Base of a Right Circular Cone of Semi-vertical Angle α is R. Show that Its Volume is 1 3 π R 3 Cot α and Curved Surface Area is πR2 Cosec α. - Mathematics

Answer in Brief

The radius of the base of a right circular cone of semi-vertical angle α is r. Show that its volume is \[\frac{1}{3} \pi r^3\] cot α and curved surface area is πr2 cosec α.

 
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Solution

\[\sin \alpha = \frac{r}{l}\]

\[ \Rightarrow r \cos ec \ \alpha = l\]

\[\tan \alpha = \frac{r}{h}\]

\[ \Rightarrow\text {  r cot } \alpha = h\]

`"volume = 1/3 pir^2h"`

`=1/3 pir^2 . r cost \ alpha`

`=1/3 pir^2 cot \ alpha`

Surface area = `pirl`      

                     = πr2 cosec α.                   

                    = πr2 cosec α.

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Q 39 | Page 83
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