Question

THE T.S.A OF CYLINDER IS 3696CM².IF THE HEIGHT OF THE CYLINDER IS TWICE THE RADIUS FIND ITS VOLUME.

Answer 1

Answer:

Maybe TSA should be 2696. Could you please confirm?

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{AnSwEr :}}}}}$

$\small{\underline{\blue{\sf{Given :}}}}$

• T. S. A of cylinder is 3696 cm²

$\rule{200}{1}$

$\small{\underline{\green{\sf{Solution :}}}}$

Let the radius of cylinder be x.

So, Height of cylinder is 2x.

We know the formula to find the T. S. A. of cylinder

$\Large{\boxed{\sf{T.S.A = 2 \pi r(r + h)}}}$

______________[Put Values]

$\sf{→3696 = 2 \times \frac{22}{7} \times x(x + 2x)} \\ \\ \sf{→\cancel{3969} \times \frac{7}{\cancel{44}} = 3x^2} \\ \\ \sf{→1176 = 3x^2} \\ \\ \sf{→\frac{1176}{3} = x^2} \\ \\ \sf{→392 = x^2} \\ \\ \sf{→x = (\sqrt{392})^2} \\ \\ \sf{→x = 20}$

∴ Radius = 20 cm

Height = 40 cm

$\rule{200}{2}$

Now,

$\Large{\star{\boxed{\sf{Volume = \pi r^2 h}}}}$

________________[Put Values]

$\sf{→Volume = \frac{22}{7} \times (20)^2 \times 40} \\ \\ \sf{→Volume = \frac{22}{7} \times 16000} \\ \\ \sf{→Volume = \frac{352000}{7}} \\ \\ \sf{→Volume = 50285.7}$

$\Large{\star{\boxed{\sf{Volume = 50285.7 \: cm^3}}}}$