Question

the curved surface area of a cylinder is 154 cm2. the total surface area of the cylinder is three times its curved surface area. find the volume of the cylinder.

Answer 1

2πrh=154
rh=49/2
r=49/2h

TSA is three time CSA
2πr(h+r)=3×154
put the value of r=49/2h
by solving you will get h=3.5

now find radius =49/2h
49/2*3.5
=7cm
volume of cylinder=πr×r×h
22/7×7×7×3.5
539cm3

Answer 2

Answer: 539 cm³

Step-by-step explanation:T.S.A = 3*154 = 462 cm²

C.S.A = 154 cm²

C.S.A = 2πrh

T.S.A = 2πr(r+h)

Now,

In T.S.A = 2πrr + 2πrh

462 = 2πrr + 2πrh

462 = 2*22/7*r*r + 154

462 – 154 = 2*22/7*r*r

308*7/2*22 = r*r

49 = r*r

R = 7 cm

Now,

C.S.A = 2πrh

154 = 2*22/7*7*h

154/44 = h

 7/2 =h

H = 3.5 cm or 7/2 cm

Now volume = πrrh

= 22/7 * 7* 7 *7/2

= 11*49

= 539 cm³

I hope it helps……