A solid cylinder has surface area of 462 sq cm Its curved surface area is one third of its total - Maths - Mensuration

Question

A solid cylinder has surface area of 462 sq cm Its curved
surface area is one third of its total surface area find the volume
of the cylinder

Vimala · Accepted Answer

Given that the total surface area of the cylinder is 462 sq.cm.Also given that curved surface area of the cylinder is one third of the total surface area.The formula for Total surface area (T.S.A) of the cylinder is $2 π r (h + r)$ , where r is the radius of the cylinder and h is the height of the cylinder.

The formula for Curved surface area (C.S.A) of the cylinder is $2 π r h$ .

Thus,

$T . S . A = C . S . A + 2 π r^{2} T . S . A = \frac{1}{3} T . S . A + 2 π r^{2} T . S . A - \frac{1}{3} T . S . A = 2 π r^{2} \frac{2}{3} T . S . A = 2 π r^{2} \frac{2}{3} (462) = 2 π r^{2} r^{2} = \frac{154 � 7}{22} r = 7$

Since the C.S.A of the cylinder is $\frac{1}{3} (462) = 154$ ,

we have,

$2 π r h = 154 h = \frac{154 � 7}{2 � 22 � 7} h = \frac{7}{2}$

Thus, height of the cylinder is $h = \frac{7}{2} c m$ and radius of the cylinder is $r = 7 c m$

Volume of the cylinder formula is

$V = π r^{2} h c u b i c u n i t s$

Thus,

the volume of the cylinder is

$V = π r^{2} h = \frac{22}{7} \times 49 \times \frac{7}{2} [a s s u m e π = \frac{22}{7}] = 539 c m^{3}$

Thus the volume of the cylinder is 539 cubic centimeter.

243

A solid cylinder has surface area of 462 sq cm.Its curved surface area is one third of its total surface area.find the volume of the cylinder.