Question

the thickness of a hollow metallic cylinder is 2 cm .it is 35 cm long and its inner radius is 12cm. find th volume of metal required to make the cylinder, assuming it is open , at either end.
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Answer 1

» Thickness of hollow cylinder is 2 cm. It is 35 cm long and it's inner radius is 12 cm.

➟ Length = 35 cm

➟ Radius = 12 cm

➟ Outer radius = 2 cm

So,

➟ Total radius = Inner radius + Outer radius

12 + 2 = 14 cm

We have to find the Volume of the metal required to make a cylinder.

Volume of metal required to make a cylinder = Volume of whole cylinder - Volume of hollow cylinder.

→ πr²h - πR²h

Here..

• r = radius of whole cylinder
• R = radius of hollow cylinder

→ 22/7 × 35 (r² - R²)

→ 22 × 5 [(14)² - (12)²]

→ 110 (196 - 144)

→ 110(52)

→ 5720

∴ 5720 cm³ is the volume of metal that is required to make a cylinder.

Answer 2

SOLUTION:-

Given:

⚫The thickness of a hollow metallic cylinder= 2cm.

⚫Inner radius= 12cm

⚫Height= 35cm

So,

Outer radius= Inner radius+thickness

outer radius= 12cm + 2cm

⚫Outer radius= 14cm

According to the question:

$Required \: volume = Whole \: cylinder \: volume - Inner \: volume \\ \\ = > \pi {R}^{2} h - \pi {r}^{2} h \\ \\ = > \pi( {R}^{2} - {r}^{2} ) \times h \\ \\ = > \frac{22}{7} ( {14}^{2} - {12}^{2} ) \times 35 \\ \\ = > 22(196 - 144) \times 5 \\ \\ = > 22 \times 52 \times 5 \\ \\ = > 5720 {cm}^{3}$

Hence,

Required volume of metal to make cylinder is 5720cm³

Hope it helps ☺️