Question

9.
The radius of the base of a right circular cylinder is increased by 75% and the height is
decreased by 50%. Find the per cent increase or decrease in the (i) volume, and (ii) curved
surface area.​

Answer 1

Step-by-step explanation:

The radius of the rate of the right circular cylinder is increased by 75% and height is decreased by 50% Find the percentage increase or deceases inits curved surface area

Curved surface area of cylinder (S

1

)=2πrh

radius is increased by 75%

So,new radius =1.75r

height is decreased by 50% so the

new heights 0.5h

Curved surface area (S

2

)=2π(1.75)r(0.5h)

=1.75πrh

Curved surface area decreases by =(

2πrh

2πrh−1.75πrh

×100)%

=(

2πrh

0.25πrh

×100)%

=12.5%

Answer 2

Let radius be r and height of the cylinder be h Therefore:-

C.S.A = 2πrh

When dimensions are changed:-

R = r+3r/4 = 7r/4

and H = h-h/2 = h/2

THerefore new C.S.A = 2π(7r/4)(h/2)=7πrh/4

Therefore change = 2πrh−7πrh/4=πrh/4

Percentage change= (πrh/4)/(2πrh)*100

= 12.5%