Question

EACH OF THE RADIUS AND THE HEIGHT OF A CONE IS INCREASED BY20%.THEN FIND THE % INCREASE IN VOLUME.

Answer 1

Let the radius of cone be r and height be h.
Therefor initial volume of cone(V) = 1/3$\pi r^{2} h$
After increasing the height and radius of cone by 20%. We get the value of:-
Radius = (100+20)% of r= 120% of r = 120/100*r = (12/10 *r)
And height = (100+20)% of h= 120% of h = 120/100*h = (12/10 *h)
Now the new Volume (Vn) will be = 1/3 * $\pi$$(12/10 *r)^{2}(12/10 *h)$
Now the percentage increased = (Vn - V )/V * 100 = 72.8%

Answer 2

radius = r
height = h
Volume = (1/3)πr²h

after 20% increase in radius and height
r' = 1.2r
h' = 1.2h
V' = (1/3)πr'²h'² = (1/3)π(1.2r)²(1.2h) = 1.728×(1/3)πr²h

increase in volume =  1.728×(1/3)πr²h - (1/3)πr²h = 0.728×(1/3)πr²h
% increase = [(0.728×(1/3)πr²h)/((1/3)πr²h)]×100
                 = 0.728×100
                 = 72.8%