Question

The curved surface area of a cylinder is 154cm. The total surface area of the cylinder is three times its curved surface area. Find the volume of the cylinder.

Answer 1

gives that

CSA of cylinder =
$2\pi rh$
=2×22/7×r×h=154

=r×h=154×7/22×1/2

=rh =49/2

And also given that

TSA=3×CSA

=2*pie*r (h+r)=3×154=462

=2×22/7×r×(h+r)=462

$rh + {r}^{2} = 462 \times 7 \div 44$
=49/2+r^2=147/2

=r^2=147/2-49/2

=r^2=(147-49)/2

=r^2=49

=r=7

volume =pie*r^2*h

=(2*pie*r*h)*r/2

= CSA*r/2

=154×7/2

=539cubic.cm

:-)hope it helps u.

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……