Question

The external radius of a pipe of metal is 4 cm and internal radius is 3 cm. If its length is 10 cm, then the volume of metal is:

• A. \( 120 \, cm^3 \)
• B. \( 220 \, cm^3 \)
• C. \( 440 \, cm^3 \)
• D. \( 1540 \, cm^3 \)

Hint:

The volume of a hollow cylinder is calculated by subtracting the inner cylindrical volume from the outer cylindrical volume using the formula: \[ V = \pi h (R^2 - r^2) \] where \( R \) is the external radius, \( r \) is the internal radius, and \( h \) is the height.

Answer 1

The Correct Option is B

Step 1: Identify given values The given data in the problem is: - External radius of the pipe, \( R = 4 \) cm - Internal radius of the pipe, \( r = 3 \) cm - Length of the pipe, \( h = 10 \) cm Step 2: Apply the formula for the volume of a hollow cylinder The volume of metal in a hollow cylinder is calculated using the formula: \[ V = \pi h (R^2 - r^2) \] Step 3: Substitute the values \[ V = \pi \times 10 \times (4^2 - 3^2) \] \[ = \pi \times 10 \times (16 - 9) \] \[ = \pi \times 10 \times 7 \] \[ = 70\pi \] Step 4: Calculate the approximate value Using \( \pi \approx 3.14 \): \[ V \approx 70 \times 3.14 = 219.8 \approx 220 \, cm^3 \] Thus, the correct answer is \( 220 \, cm^3 \).