Conical's a = 18.7 cms, surface area LSA = 602.8 (cms)2 , find out volume of conical ?

Answer 1

height = 18.7 = cm

Area = 602.8 cm^2 = pi(r)L

rL =602.8/3.14 = about 192

L = 192/r

L^2 = r^2 +h^2

(192/r)^2 = r^2 + 18.7^2

let x =r^2

192^2/x = x + 18.7^2

192^2 = x^2 + (18.7^2)(x)

36846 = x^2 + 349.69x

x^2 +349.69x -36846

use the quadratic formula

x = -349.69/2 +/-(1/2)sqr(349.69^2 +4(36846))

ignore the negative square root

r =sqrx = sqr[-349.69/2 +.5sqr(349.69^2 +4(36846))

volume = 1/3)(h)(pi)r^2= 18.7/3)(3.14)r^2

= (18.7/3)(3.14)x= 6.23(3.14)(-174.85 + .5(519.3)

= 19.6(-174.85+259.7)

=19.6(84.85)

=about 1,664 cm^3