Question

A hollow metal pipe whose external and internal diameters are 6.3cm and 2.8cm respectively. The height is 3.5m long. Calculate the volume of the metal used to make the pipe.

A) 81.83 cm³
B) 405.29 cm³
C) 1,155.75 cm³
D) 5,776.31 cm³

Answer 1

The volume of the metal used to make the pipe is 87.3444 cm³.

Step-by-step explanation:

To calculate the volume of the metal used to make the pipe, we need to find the difference between the volumes of the outer and inner cylinders.

The outer cylinder's volume can be calculated using the formula V = πr²h, where r is the radius and h is the height. In this case, the radius is half of the external diameter, so the outer radius is 6.3 cm ÷ 2 = 3.15 cm. Plugging these values into the formula, we get V_outer = 3.142 × (3.15 cm)² × 3.5 m = 110.26925 cm³.

The inner cylinder's volume can be calculated in the same way, using the inner radius. The inner radius is half of the internal diameter, so the inner radius is 2.8 cm ÷ 2 = 1.4 cm. Plugging these values into the formula, we get V_inner = 3.142 × (1.4 cm)² × 3.5 m = 22.92485 cm³.

To find the volume of the metal used to make the pipe, we subtract the volume of the inner cylinder from the volume of the outer cylinder: V = V_outer - V_inner = 110.26925 cm³ - 22.92485 cm³ = 87.3444 cm³.

Therefore, option A) 81.83 cm³ is the correct answer.