The ratio between the curved surface area and the total surface area of right cy

Question

The ratio between the curved surface area and the total surface area of right cylinder is 2:3 and the total surface area is 924 cm

^{2}

. What is the volume of the cylinder?

Options:

A . 2156 cc

B . 2183 cc

C . 2492 cc

D . None of these

Answer: Option A
:
A
Solution:- Total surface Area:

\frac{2 π r^{2} + 2 π r h}{2 π r h} = \frac{3}{2} \Rightarrow 1 + \frac{r}{h} = \frac{3}{2} \Rightarrow \frac{r}{h} = \frac{1}{2} \Rightarrow h = 2 r

TSA:

(2 π r^{2} + 2 π r h)

= 924

\Rightarrow (2 π r^{2} + 2 π r \times 2 r)

= 924

\Rightarrow

r = 7 and h = 14
Volume =

π r^{2} h = \frac{22}{7} \times 7 \times 7 \times 14

= 2156
Option(a).

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