Question

6. The thickness of a hollow metallic cylinder is 2 cm. It is 35 cm long and its inner
radius is 12 cm. Find the volume of metal required to make the cylinder, assuming
itis open, at either end.​

Answer 1

$\large\underline{\boxed{\bold\red{Question}}}$

The thickness of a hollow wooden cylinder is 2 cm. It is 35 cm long and its inner radius is 12 cm. Find the volume of the wood required to make the cylinder, assuming it is open at either end.

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$\large\underline{\boxed{\bold\green{Given}}}$

$\pink {:\leadsto}\green{Inner \: radius \: r1 = 12cm}$

$\pink{:\leadsto}\green{outter \: radius \: r2 = 12+2}$

$\pink{:\leadsto}\green{outter \: radius \: r2 = 14}$

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$</p><p>\large\underline{\boxed{\bold\purple{Formula}}}[\tex]</p><h3><strong>Volume of required cylinder = volume of inner surface - volume of outer </strong><strong>surface</strong></h3><p><strong>[tex]\purple{π(r1²+r2²)h}$

$\purple{ (a+b)² = (a+b) × (a-b)}$

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$\pink{:\leadsto}\orange{\dfrac{22}{7}×[(14)²-(12)²]×35}$

$\pink{:\leadsto}\orange{\dfrac{22}{7}×[(14-12)²]×35}$

$\purple{Using \: (a+b)² = (a+b) × (a-b)}$

$\pink{:\leadsto} \orange{\dfrac{22}{7}×[(14+12)(14-12)]×35}$

$\pink{:\leadsto}\large\orange{22×26×2×5}$

$\large\pink{:\leadsto}\orange{572 \times 10}$

$\large\pink{:\leadsto}\orange{5720 \: cm³}$

[Hope this helps you.../]