Question

${\huge{\underline{\underline{\mathfrak{QUESTION}}}}}$

The volume of a cylinder is 6538 cubic centimetres and its height is 28 cm. find its radius.

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Answer 1

${\huge{\underline{\underline{\mathfrak{QUESTION}}}}}$

The volume of a cylinder is 6538 cubic centimetres and its height is 28 cm. find its radius and the curved surface area.

${\huge{\underline{\underline{\mathbb{ANSWER}}}}}$

${\huge{\underline{\mathbb{GIVEN}}}}$

$\longmapsto\sf Volume\ of\ cylinder\ =\ 6538\ {cm}^{3}$

$\longmapsto\sf Height\ of\ cylinder\ =\ 28 cm$

${\huge{\underline{\mathbb{TO\FIND}}}}$

$\longmapsto\sf Radius\ of\ cylinder\ =\ ??$

$\longmapsto\sf Curved\ Surface\ Area\ =\ ???$

${\huge{\underline{\mathbb{FORMULA\ USED}}}}$

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

$C.S.A.\ of\ Cylinder\ =2\pi rh$

${\huge{\underline{\mathbb{SOLUTION}}}}$

Let the radius be r m

$According\ to\ given\ conditions$

$Volume\ of\ cylinder\=6538{cm}^{3}$

$=>\pi {r}^{2}h=6538$

$=>{r}^{2}=\frac{6538×7}{22×28}$

$=>r=\sqrt{72.25}$

Hence, radius= $\boxed{8.5}$

Answer 2

Given:-

volume of cylinder= πr²h=6538cm³

Height of cylinder= 28 cm

To find :- radius of cylinder.

Solution:-

radius of cylinder

$\pi {r}^{2} h = \frac{22}{7} \times {r }^{2} \: \times 28 \\ \frac{6538}{ \frac{22}{7} \times 28 } \\{r }^{2} =\root 72.25 \\ {r }^{2} = 8.6cm \\ csa \: of \: cyliner = 2\pi \: rh \\ 2 \times \frac{22}{7} \times 8.6 \times 28 \\ 1519.6cm {}^{2}$