Question

A cylindrical tank has a capacity of 6160 metre cube. Find its depth if its radius is 14 m. also find the cost of painting it's curved surface at Rs 3 per metre square. *​

Answer 1

Given:-

• Volume of cylinder=6160cubic.metre
• Radius = 14m

To Find:-

• Height of cylinder
• Cost of painting it's curved surface Area

Solution :-

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

$:\implies\sf \dfrac{22}{\cancel{7}}\times \cancel{14}\times 14\times h= 6160\\ \\ \\ :\implies\sf 616\times h=6160 \\ \\ \\ :\implies\sf h=\cancel{\dfrac{6160}{616}}\\ \\ \\ :\implies\sf \ Height = \underline{\boxed{\red{\sf\ 10m}}}$

• CSA of cylinder -

$\underline{\boxed{\sf\ CSA\ of\ cylinder=2 \pi r h}}$

$:\implies\sf\ CSA= 2\times \dfrac{22}{\cancel{7}}\times \cancel{14}\times 10\\ \\ \\ :\implies\sf \ CSA= 44\times 20\\ \\ \\ :\implies\sf \ CSA= 880m^2$

• Cost of painting -

$\dashrightarrow\sf\ cost\ of\ painting \ of \ 1m^2= Rs.3\\ \\ \\ \dashrightarrow\sf Cost\ of\ 880m^2= 880\times 3\\ \\ \\ \dashrightarrow\sf\ Cost\ of\ painting=\underline{\boxed{\purple{\sf\ Rs.\ 2640}}}$

Answer 2

Given:

• Capacity of a tank= Volume= 6160m
• Radius= 14m
• Cost of painting = Rs. 3 per meter square

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Need to Find:

• The depth= Height= ?
• The cost of liamtimg it's curved surface area=?

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Solution:

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

$\implies \: 6160 {m}^{3} = \dfrac{22}{7} \times 14 \times 14 \times h$

$\implies \: 22 \times 2 \times 14 \times h \: {m}^{2} = 6160 {m}^{3}$

$\implies \: h = \dfrac{6160}{616} m$

$\red{\bold{\implies \: h = 10m}}$

Depth = 10m

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Curved surface of cylinder:

$= 2\pi \times r \times h$

$= 2 \times \dfrac{22}{7} \times 14 \times 10 {m}^{2}$

$= 2 \times 22 \times 2 \times 10 {m}^{2}$

$\boxed{\blue{ = 880 {m}^{2}}}$

The cost= Curved Surface area× The cost per meter

→ Cost=880× 3 Rupees

$\red{\bold{→Cost= 2640Rupees}}$