Question

a cylinder open at both ends is made of 2cm thick steel . if the inner radius of the cylinder is 8 cm. find the volume of the steel used ,if the cylinder is 42cm long​

Answer 1

Answer

4752 cm³ is the volume of steel required to make the cylinder.

$\rule{200}2$

Step-by-step explanation

Given:-

• Thickness of cylinder = 2 cm
• Inner radius of cylinder = 8 cm
• Length of cylinder = 42 cm
• Outer radius of cylinder = 8 + 2 = 10 cm

Find:-

Volume of steel used.

Solution:-

Volume of steel required to make the cylinder = Volume of cylinder - Volume of hollow cylinder

We know that volume of cylinder is πr²h

So,

Let the -

• Inner radius of cylinder be "r"
• Outer radius of cylinder be "R"

Substitute the known values in above formula

⇒ πR²h - πr²h

⇒ πh(R² - r²)

⇒ 22/7 × 42 [(10)² - (8)²]

⇒ 22 × 6 [100 - 64]

⇒ 132 (36)

⇒ 4752 cm³

Answer 2

Solution :

A cylinder in open at boths ends and it is made of 2 cm thick steel.

This means the base of the cylinder is in the shape of ring.

We know that :

Volume of the steel = Area of the base which in the shape of ring * Height

So, let's first find out what is the area of the base

Inner radius of the base ring r = 8 cm

Thiness of the steel = 2 cm

Outer radius of the vase ring R = r + thikness of steel = 8 + 2 = 10 cm

Area of the base ring = π(R + r)(R - r)

= 22/7 * (10 + 8)(10 - 8)

= 22/7 * 18 * 2

= 22/7 * 36

= 792/7 cm²

Now let's find the Volume of the steel

Area of the base ring = 792/7 cm²

Height of the cylinder = 42 cm

Volume of the steel used = Area of the base ring * Height

$= \dfrac{792}{7} \times 42$

= 792 * 6

= 4752 cm³

Hence, volume if steel used is 4752 cm³.