Question

the sum of the radius of base and the height of solid cylinder is 37 cm. if the total surface area of the solid cylinder is 1628cm sq. Find the volume of cylinder?

Answer 1

Greetings,
The answer to your question is typed below↓...
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Given: radius [r] + height [h] = 37cm
          & CSA =1628 sq cm.

To find volume...
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Solution:

Take: r= 37 - h;

and as CSA = 2*22/7*rh

⇒2 x 22/7 x 37-h x h =1628
⇒6.28 x (37h - h²) = 1628
⇒232.47h - 6.28h² =1628
⇒6.28h² - 232.47h + 1628 = 0
on solving quadratic; we get:
h=27.6
r=9.3

Volume = 22/7 x r² x h

⇒ 22/7 x 9.3² x 27.6
⇒7500 c. cm
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Ps. : Enjoy;)