Question

The curved surface area of a cylinder is
3850 sq.cm and the curcumference of the base
is 220cm. Calculate:
a] The height of a cylinder
b] Volume of the cylinder​

Answer 1

Given :-

The C.S.A of cylinder is 3850 sq.cm

Circumference of base =220

To find :-

The height of cylinder

Volume of cylinder

Now ,

A.T.Q

Formula used :-

$\boxed{\sf{C.S.A\:of\: cylinder=2\pi r h}}$

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

First find the Height of cylinder

● Circumference = 2πr

$\sf\implies 2\pi r h=C.S.A\\ \\ \sf \bullet Put\:the\:value\:of\: circumference= 220cm\\ \\ \sf\implies 220\times h=3850\\ \\ \sf\implies h=\cancel{\dfrac{3850}{220}}\\ \\ \sf\implies h=17.5cm$

• Now the Volume of cylinder
• we have to find the radius of cylinder to find volume

So find the value of r

$\sf\implies 2\pi r h=3850\\ \\ \sf\implies 2\times \dfrac{22}{7}\times r\times 17.5=3850\\ \\ \sf\implies \dfrac{2\times 22\times 17.5}{7}\times r=3850\\ \\ \sf\implies \cancel{\dfrac{770}{7}}\times r=3850\\ \\ \sf \implies 110\times r=3850\\ \\ \sf\implies r= \cancel{\dfrac{3850}{110}}\\ \\ \sf \implies r= 35cm$

Now finally find the volume of cylinder

$\sf\implies Volume\:of\: cylinder=\pi r{}^{2} h\\ \\ \sf\implies Volume\:of\: cylinder= \dfrac{22}{\cancel7}\times \cancel{35}\times 35\times 17.5\\ \\ \sf\implies Volume\:of\: cylinder=22\times 5\times 35\times 17.5\\ \\ \sf\implies Volume =67375cm{}^{3}$

$\underline{\dag{\sf{Height\:of\: cylinder=17.5cm}}}$

$\underline{\dag{\sf{Volume\:of \: cylinder= 67375cm{}^{3}}}}$

Answer 2

☑️ Given That :

• Curved Surface Area of cylinder (C.S.A.) = 3850 sq. cm
• Circumference = 220 cm

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☑️ To Find :

• (a) Height of the Cylinder
• (b) Volume of the Cylinder

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☑️ As we know that :

$\implies{\large{\boxed{\sf{\underline{\underline{\blue{ C.S.A. \:Of \: The \: Cylinder = 2πrh }}}}}}}$

$\implies{\large{\boxed{\sf{\underline{\underline{\blue{ Volume \: Of \: The \: Cylinder = π{r}^2h}}}}}}}$

$\implies$$\large{\boxed{\sf{\underline{\underline{\blue{ Circumference = 2πr }}}}}}$

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$\huge{\{\green{\boxed{\boxed{\sf{\underline{\underline{\pink{.SoLutiOn.}}}}}}}}$

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(a) To Find the height of the cylinder,

Here,

C.S.A. of the cylinder = 2πrh

$\implies$ 3850 = Circumference × h

$\implies$ 3850 = 220 × h

$\implies$ h = 3850/220

$\implies$ $\large{\boxed{\sf{\underline{\orange{ h = 17.5 \: cm}}}}}$

$\therefore$ The Required Height of the cylinder is 17.5 cm.

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(b) To Find the Volume of the Cylinder,

We need to Find the value of r

Here,

$\implies$ 2πrh = 3850

$\implies$ $2 \times \frac{22}{7} \times r\times 17.5 = 3850$

$\implies$ $r = \frac{3850 \times 7}{2 \times 22 \times 17.5}$

$\implies$ $r = \frac{26950}{770}$

$\implies$ r = 35 cm

Now,

Volume Of The Cylinder = π${r}^2$h

on putting all the required values

$\implies\: Volume \:Of\: The\: Cylinder \:= \frac{22}{7} \times 35 \times 35 \times 17.5$

$\implies$ Volume of The Cylinder = $\frac{471625}{7}$

$\implies{\large{\boxed{\sf{\underline{\orange{Volume \: Of \: The \: Cylinder = 67375\:{cm}^3}}}}}}$

$\therefore$ The Required Volume of the Cylinder Will be 67375 cubic cm.

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⋰ Hope It Will Be Helpful To You Mate ⋱

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