Question

The radius and the height of the right circular cone are in the ratio 4:3 and its volume is 2156cm3 (3 means cube).Find the csa of the cone.

Answer 1

you can also solve it by taking h=4/3r

Answer 2

THANKS FOR THE QUESTION !

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GIVEN :

DIMENSIONS OF CONE :

=> RADIUS / HEIGHT = 4 / 3

VOLUME OF THE CONE :

=> 2156 CM^3

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TO FIND :

=> CURVED SURFACE AREA OF CONE

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LET,

=> RADIUS = 4X

=> HEIGHT = 3X

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VOLUME OF CONE :

=> 1/3 π * R^2 * H

=> 1/3 * 22/7 * ( 4X )^2 * 3X

=> 22 / 21 * 16X^2 * 3X

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BUT VOLUME IS GIVEN :

=> 2,156 CM^3

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=> 2,156 = 22 / 21 * 16X^2 * 3X

=> 2,156 * 21 / 22 = 16X^2 * 3X

=> 98 * 21 = 48 X^3

=> 2,058 = 48 * X^3

=> X^3 = 2,058 / 48

=> X^3 = 42.875

=> X = 3√ 42.875

=> X = 3.5

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RADIUS :

=> 4X

=> 4 * 3.5

=> 14

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HEIGHT :

=> 3X

=> 3 * 3.5 .

=> 10.5

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FOR FINDING CURVED SURFACE AREA:

L( SLANT HEIGHT ) :

=> L^2 = H^2 + R^2

=> L^2 = ( 10.5 )^2 + ( 14 ) ^2

=> L^2 = 110.25 + 196

=> L^2 = 306.25

=> L = √ 306.25

=> L = 17.5

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CURVED SURFACE AREA OF CONE :

=> π * R * L

=> 22 / 7 * 14 * 17.5

=> 44 * 17.5

=> 770 SQ.CM

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HOPE IT WILL HELP U.....

THANKS AGAIN.....

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