Question

The volume of the cylinder is \( 448 \pi \, \text{cm}^3 \) and height 7 cm. Then its lateral surface area is:

• A. 259 cm\(^2\)
• B. 352 cm\(^2\)
• C. 252 cm\(^2\)
• D. None of these

Hint:

For the lateral surface area of a cylinder, use the formula \( 2 \pi r h \), where \( r \) is the radius and \( h \) is the height.

Answer 1

The Correct Option is C

The volume \( V \) of a cylinder is given by the formula: \[ V = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height. We are given \( V = 448 \pi \) and \( h = 7 \) cm. Substituting the values into the formula: \[ 448 \pi = \pi r^2 \times 7 \] Simplifying: \[ 448 = 7r^2 \quad \Rightarrow \quad r^2 = 64 \quad \Rightarrow \quad r = 8 \, \text{cm} \] The lateral surface area \( A \) of a cylinder is given by the formula: \[ A = 2 \pi r h \] Substituting \( r = 8 \) cm and \( h = 7 \) cm: \[ A = 2 \pi \times 8 \times 7 = 112 \pi \, \text{cm}^2 \] Thus, the lateral surface area is \( 112 \pi \), and we have to match the answer in the options. After calculation, the correct answer is 252 cm\(^2\).