Question

A cylinder is made of metal having thickness 2 cm. The outer diameter of the cylinder is 14 cm and
height of the cylinder is 14 cm. Find the capacity of cylinder and also volume of the metal used.​

Answer 1

Step-by-step explanation:

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Answer 2

Question :-

A Cylinder is made of Metal Having Thickness 2 cm. The Outer Diameter of the Cylinder is 14 cm and the Height of the Cylinder is 14 cm.

Find the Capacity of the Cylinder and also the Volume of the Metal used.

Solution :-

Outer Diameter of the Cylinder = 14 cm

∴ Outer Radius of the Cylinder, R = 14/2 cm = 7 cm

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Thus, the Inner Radius, r of the Cylinder would be -

Inner Radius, r = (Outer Radius of the Cylinder - Thickness of the Cylinder)

Inner Radius, r ⇒ (7 cm - 2 cm) = 5 cm

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∴ The Capacity of the Cylinder, V = πr²h Cubic Units

$\begin {aligned} \implies \bold {Capacity\: of\: the \:Cylinder, V} & = (\frac {22}{7} \times 5^2 \times 14)\:cm^3\\\\& \Rightarrow (\frac{22}{7} \times 25\times 14)\: cm^3\\\\& \Rightarrow (22 \times 25 \times 2) = \bold {1,100\: cm^3} \end{aligned}$

Volume of the Metal = (Volume of the Outer Cylinder - Volume of the Inner Cylinder)

$\begin {aligned} \implies \bold {Volume\: of\: the\: Metal, V} & = (\frac{22}{7} \times 7^2 \times 14) - 1,100\: cm^3\\\\& \Rightarrow (\frac{22}{7} \times 49 \times 14) - 1,100\: cm^3\\\\& \Rightarrow (2,156 - 1,100)\: cm^3 \\\\ & = \bold {1,056\: cm^3} \end {aligned}$

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$\mathfrak {Hence, The\: Capacity\: of\: the \; Cylinder\: is = \bold {1,100\: cm^3}\: and,}\\\\\mathfrak {The\: Volume\: of\: the\: Metal = \bold {1,056\: cm^3}}$

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