Math, asked by vanshikapatel6396, 11 months ago

The metal with the volume of 1496 cm is used to cast a pipe of length 28 CM if the internal radius of pipe is 8 cm find its outer radius​

Answers

Answered by Cosmique
14

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GIVEN:

the \: volume \: of \: metal \\  \: used \: to \: cast \: pipe =  1496 {cm}^{3}

length \: of \: pipe  = 28 \: cm  = h\\  internal \: radius \: of \: pipe = 8 \: cm = r

TO FIND:

Outer radius of pipe =?

SOLUTION:

LET,

outer radius of pipe be x

then,

Volume of hollow metallic pipe will be

volume with outer radius - volume with inner radius

I. e,

\pi {x}^{2} h \:  - \pi {r}^{2} h  \\  \\ (that \: is \: ) \\ \pi \: \times  h( {x}^{2}  -  {r}^{2} )

so,

1496 =  \frac{22}{7} \times 28 \times  ( {x}^{2}  -  {8}^{2} ) \\  \\ 1496 = 22 \times 4 \times ( {x}^{2}  - 64) \\  \\  \frac{1496}{22 \times 4}  =  {x}^{2} - 64 \\  \\ 17 =  {x}^{2}  - 64 \\  \\  {x}^{2}   = 17 + 64 \\  {x}^{2}  = 81 \\  \\ x = 9

SO THE OUTER RADIUS OF THE PIPE WILL BE 9 CM.

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