Question

31. a solid cylinder has total surface area of 462 cm2 . if total surface area of the cylinder is thrice of its curved surface area. then the volume of the cylinder is:

Answer 1

Volume of a solid sylinder = $\pi r^2 h$

Total surface area = $2 \pi r(r+h)$

Curved surface area = area excluding bases = $2\pi rh$

We are given total surface area as 462 sq cm and also a relation between total surface area and curved surface area.

3Curved surface area = total surface area

i.e. $2 \pi r(r+h)$=3$2\pi rh$

Simplify to get

$4 \pirh = 6\pi r^2 :</p><p>2h= 3r:$

Use this in the total surface area formula.

$2\pi r(r+h) = 486:</p> <p>2\pi r(r+\frac{3r}{2} ) = 486:</p><p>r = 5.563 cm and h = 3r/2 = 8.346cm$

Volume = π(5.563)(5.563)(8.346) = 811.01 cubic cm.

Answer 2

$\huge{\mathfrak{\red{Answer}}}$

Curved surface area = total surface area / 3.

Curved surface area = 462/3 = 154.

Rest of area = 462 - 154 = 308.

$\longrightarrow$2πr^2 = 308.

$\longrightarrow$r^2 = 308 x 7 / 44 = 49.

$\longrightarrow$r = 7.

2πrh = 154.

h = 154 / 2 x 22 = 7/2.

$\longrightarrow$Volume = πr^2 h = (22/7) x (7^2) x (7/2) = 539.

$\rm Volume = 539 cm^3$