Question

The CSAof a cylinder is 1000 centimetre square and its diameter is 20 cm find the height and volume

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

$\\{\bold{\therefore Height=\frac{175}{11}}}$

${\bold{\therefore Volume=5000\:cm^{3}}}$

${\bold{\underline{\underline{Step-by-step\:explanation}}}}$

$\underline \bold{Given : } \\ \implies C.S.A\: of \: cylinder = 1000 \: {cm}^{2} \\ \\ \implies Diameter \: of \: cylinder = 20 \: cm \\ \\ \underline \bold{To \: Find : } \\ \implies Height(h) = ? \\ \\ \implies Volume = ?$

• According to given question :

$\bold{Using \: formula \: of \: C.S.A \: of \: cylinder : } \\ \implies C.S.A \: of \: cylinder = 2\pi rh \\ \\ \implies 1000 = 2 \times \frac{22}{7} \times 10 \times h \\ \\ \implies \frac{1000 \times 7}{2 \times 22 \times 10} = h \\ \\ \implies h = \frac{700}{44} \\ \\ \bold{ \implies h = \frac{175}{11} \: cm} \\ \\ \bold{Using \: formula \: of \: Volume \: of \: cylinder: } \\ \implies Volume \: of \: cylinder = {\pi r}^{2} h \\ \\ \implies Volume = \frac{22}{7} \times 10 \times 10 \times \frac{175}{11} \\ \\ \implies Volume = 2 \times 100 \times 25 \\ \\ \bold{\implies Volume = 5000 \: {cm}^{3} }$

Answer 2

SOLUTION:

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Given:

•The curved surface area of a cylinder is 1000cm².

•Dimeter of the cylinder= 20cm.

To find:

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• The height of the cylinder &
• The volume of the cylinder.

Explanation:

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•Dimeter of the cylinder= 20cm

•Radius of the cylinder= d/2

•Radius of the cylinder= 20/2

•Radius of the cylinder= 10cm

• C.S.A of cylinder= 1000cm².

We know that, formula of the curved surface area of cylinder;

=) 2πrh

Therefore,

$= > 2 \times \frac{22}{7} \times 10 \times h = 1000 \\ \\ = > \frac{44}{7} \times 10 \times h = 1000 \\ \\ = > h = \frac{1000 \times 7}{44 \times 10} \\ \\ = > h = \frac{100 \times 7}{44} \\ \\ = > h = \frac{700}{44} cm \\ \\ = > h = \frac{175}{11} cm$

Now,

Formula: Volume of the cylinder;

Formula: πr²h

Therefore,

$Volume \: of \: the \: cylinder = \frac{22}{7} \times 10 \times 10 \times \frac{175}{11} \\ \\ Volume \: of \: the \: cylinder = (2 \times 100 \times 25) {cm}^{3} \\ \\ Volume \: of \: the \: cylinder = (200 \times 25) {cm}^{3} \\ \\ Volume \: of \: the \: cylinder = 5000 {cm}^{3}$

Thus,

• Height of the cylinder= 175/11cm.
• Volume of the cylinder= 5000cm³

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