Question

The radius and height of a right circular cone are in the ratio 3:4 and it's volume is 2156cm. Find the CSA and TSA of the cone

Answer 1

Hey !!

Here is your answer ... ⬇⬇

let radius and height of the cone be( r ) and( h ) respectively.

Given that ratio of radius and height is 3:4
so,
r/h = 3/4

h = 4r/3 ------- ( 1 )

Volume of Cone is 2156 cm^3.
Volume = 2156
1/3 πr^2 h = 2156
1/3 × 22/7 × r^2 × 4r/3 = 2156
88r^3 = 2156 × 63
88r^3 = 135828
r^3 = 135828/88
r^3 = 1543.5
r = 11.55 cm

Put the value of ( r ) in eq. ( 1 )

h = 4( 11.55 )/3
h = 46.2/3
h = 15.4 cm

Now, find slant height ( l ).

l^2 = r^2 + h^2
l^2 = ( 11.55 )^2 + ( 15.4 )^2
l^2 = 133.4 + 237.16
l^2 = 370.56
l = √370.56
l = 19.24 cm

Find C.S.A

C.S.A = πrl
= 22/7 × 11.55 × 19.24
= 4888.88/7
= 698.41 cm^2

Find T.S.A

T.S.A = πr ( l + r )
= 22/7 × 11.55 ( 19.24 + 11.55 )
= 254.1/7 (30.79 )
= 254.1 × 4.39
= 1115.49 cm^2


HOPE IT HELPS YOU.....

THANKS ^-^