Question

The volume of a cylindrical vessel is 448 cubic cm and height is 7 cm. Find the surface area of the vessel if it is closed at bottom

Answer 1

Question :

The volume of a cylindrical vessel is 448 cubic cm and height is 7 cm. Find the surface area of the vessel if it is closed at bottom.

Solution :

Given : Cylinder height ,h = 7 cm

Volume of cylindrical vessel= 448cm^3

Let the radius of the base of the cylinder be r cm.

We know that ,

$\sf \: volume \: of \: cylinder = \pi \: r {}^{2} h$

$\implies\:\sf \:\pi\: {r}^{2} h = 448$

$\implies\:\sf \: {r}^{2} h =\dfrac{448\times7}{22}$

$\implies\:\sf \: {r}^{2}= \dfrac{448\times7}{22\times7}$

$\implies\:\sf \: {r}^{2} =20.3$

$\implies\:\sf \: r\approx\:4.5\:cm$

Lateral surface area =$\sf \:2 \pi \: rh$

$\sf \:= 2\times\:\dfrac{22}{7}\:\times\:4.5\times\:7$

$\sf \: = 198cm{}^{2}$

and Base area $= \sf \: \pi \: {r}^{2}$

$\sf \:= \dfrac{22}{7}\times4.5{}^{2}$

$\sf \:= \dfrac{445.5}{7}$

$\sf \: \approx\:63.64 {cm}^{2}$

Therefore,Surface area of the vessel if it is closed at bottom

= lateral surface area + base area

$\sf \:= (198+63.64)cm{}^{2}$

$\sf \:= 261.64cm{}^{2}$

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Formula's Related to cylinder :

$1)\sf \: volume \: of \: cylinder = \pi \: r {}^{2} h$

$2) \sf \: Lateral\: surface\:\area\: cylinder = 2\pi \: r h$

Answer 2

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