Question

radius of the base of right circular cylinder is increased by 75% and height is decreased by 50% find the percent increase or decrease on curve surface

Answer 1

Let the radius and height of the cylinder be r and h

Curved surface area of cylinder = 2pie rh

Given radius increased by 75%, hence new radius = r+3r/4 = 7r/4

Height is decreased by 50%, hence new height = h-h/2 = h/2

Curved surface area of new cylinder = 2pie. 7r/4. h/2

Decrease in curved surface area = 2pie rh -  2pie. 7r/4. h/2= pie rh

Percent decrease  = (pie rh/2pie rh) . 100 = 50%

Answer 2

Answer:

12.5%

Step-by-step explanation:

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%