Question

A hollow metal cylindrical pipe has an outer diameter of 10 cm and inner diameter of 8 cm . find the volume of the metal used if it is 21 cm long.​

Answer 1

Answer:

Find the volume with diameter = 6 cm

Radius = Diameter÷2

Radius 6÷2 = 3 cm

Volume = nr²h

Volume = π[3)²(21) = 594 cm³

Find the volume with diameter = 10 cm

Radius = Diameter÷2

Radius = 10 ÷ 2 = 5 cm

Volume = mr²h

Volume = T(5)²(21) = 1650 cm³

Find the volume of the metal used:

Volume = 1650 - 594 = 1056 cm³

Answer: The volume of the metal used is 1056 cm³

Answer 2

ANSWER:

Given:

• Hollow metal cylindrical pipe
• Outer diameter(D) = 10cm
• Inner diameter(d) = 8cm
• Height(h) = 21cm

To Find:

• Volume of metal used.

Diagram:

$]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(4,0){2}{\line(0,1){6}}\multiput(1,0)(2,0){2}{\line(0,1){6}}\multiput(0,0)(0,6){2}{\qbezier(0,0)(2,-0.6)(4,0)}\multiput(0,0)(0,6){2}{\qbezier(0,0)(2,0.6)(4,0)}\multiput(1,0)(0,6){2}{\qbezier(0,0)(1,-0.2)(2,0)}\multiput(1,0)(0,6){2}{\qbezier(0,0)(1,0.2)(2,0)}\multiput(2,0.07)(0,0.3){20}{\line(0,1){0.2}}\multiput(2,4)(0.3,0){7}{\line(1,0){0.2}}\multiput(2,2)(-0.27,0){4}{\line(-1,0){0.2}}\put(1.2,1.5){\bf\large 4cm}\put(3.2,3.45){\bf 5cm}\put(1.2,3){\bf 21cm}\end{picture}$

Solution:

We know that,

⇒ Volume of a hollow cylinder = π(R² - r²)h

Here, R is the outer radius, r is the inner radius and h is the height.

According to this question,

⇒ R = D/2 = 10/2 = 5cm,

⇒ r = d/2 = 5/2 = 4cm.

So,

⇒ Volume of the hollow cylindrical pipe = π(R² - r²)h

⇒ Volume of the hollow cylindrical pipe = 22/7 × (5² - 4²)21

⇒ Volume of the hollow cylindrical pipe = 22 × (25 - 16) × 3

⇒ Volume of the hollow cylindrical pipe = 22 × 9 × 3

⇒ Volume of the hollow cylindrical pipe = 594cm²

Formula Used:

• Volume of a hollow cylinder = π(R² - r²)h