Question

the radius of the base of a right circular cylinder decreased by 25 percent and height is increased by 50 percent . find the percent decrease or increase in its CSA. please telll me fast right now​

Answer 1

The per cent decrease or increase in the CSA of the right circular cylinder is 12.5%.

Step-by-step explanation:

Let’s assume:

A1 = CSA of the original right circular cylinder

r1 = radius of the base of the original right circular cylinder  

h1 = height of the original right circular cylinder

A2 = New CSA of the right circular cylinder

r2 = new radius of the base of the cylinder = r1 - (25%*r1) = $\frac{75}{100}$*r1 = (¾)r1

h2 = new height of the cylinder = h1 + (50%*h1) = $\frac{150}{100} * h1 = <strong>\frac{3}{2}$*h1

Now,  

The CSA of the original right circular cylinder, A1 = 2πr1h1 ….. (i)  

And

The New CSA of the right circular cylinder, A2, is given by,

= 2πr2h2

= 2π*(3r1/4)*(3h1/2)  

= 2πr1h1 * $\frac{9}{8}$ ….. (ii)

Thus,

The per cent decrease or increase in the CSA of the right circular cylinder is,

= $\frac{A2 - A1}{A1} * 100$

= [{(2πr1h1 * (9/8)) – (2πr1h1)} / {2πr1h1}] * 100

= [9/8 - 1] * 100

= [(9-8)/8] * 100

= (1/8) * 100

= 12.5%

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