Question

the thickness of a hollow metallic cylinder is 2 centimetre it is 35 cm long and its inner radius 12 cm find the volume of metal required to make the cylinder assuming it's open at either end​

Answer 1

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$\large{\underline{\sf{\red{Required\:Answer:}}}}$

$\large\boxed{\underline{{\sf {5720 \: cm}^{2}}}}$

Given:-

• Inner radius of cylinder r = 12 cm.

• Thickness = 2 cm.

• Height = 35 cm.

To Find:-

• Other radius.

• Volume of metal required to make cylinder.

Solution:-

Other radius R = ${\sf{12 + 2 = 14 \: cm }}$

It is a hollow cylinder.

$\boxed{\underline{\pink{\sf Volume \: of \: metal \: required \: to \: make \: cylinder = outer \: volume - inner \: volume}}}$

$\purple{\implies\:\:}$ ${\sf{ \pi R^{2} h - \pi r ^{2} h }}$

$\purple{\implies\:\:}$ ${\sf{\dfrac{22}{7} \times 35 \times (14 ^{2} - 12 ^{2}) }}$

$\purple{\implies\:\:}$ ${\sf{{5720 \: cm}^{2} }}$

✤ Hence, the volume of metal required to make the cylinder, assuming it is open, at either end = ${\sf{ {5720 \: cm}^{2} }}$

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Answer 2

Answer:

5278 cm³

Step-by-step explanation:

Assume that the outer layer of cylinder is a cuboid

Find circumference of circle

= 2 × π × r

= 2 × π × 12 cm

= 75.4 cm

Find volume of the cover

= l × b × h

= 35 cm × 75.4 cm × 2 cm

= 5278 cm³