Question

The ratio of total surface area to curved surface
area of a cylinder is 3:2. If the total surface
area is 8316cm² . Find its volume
​

Answer 1

Answer:

Let 3x and 2x respectively.

3x+2x=8316

5x=8316

x= 1663.2

Answer 2

The volume of cylinder is 58212 cm³

Step-by-step explanation:

The ratio of total surface area to curved surface  area of a cylinder is 3:2

Total surface area of cylinder,  $T=2\pi rh+2\pi r^2$

Curved surface area of cylinder, $C=2\pi rh$

If the total surface  area is 8316 cm²

$2\pi rh+2\pi r^2=8316$

$\dfrac{T}{C}=\dfrac{3}{2}$

$C=\dfrac{2}{3}\times T$

$C=\dfrac{2}{3}\times 8316$

$C=5544$

$2\pi rh=5544$

But $2\pi rh+2\pi r^2=8316$

$5544+2\pi r^2=8316$

$r^2=441$

$r=21\ cm$

$h=42\ cm$

Volume of cylinder $=\pi r^2h$

                                $=\pi\times 21^2\times 42$

                                $=58212\ cm^3$

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