Question

A right circular cylinder has radius 7 cm and height 10 cm. Find its curved surface area. (Take \(\pi=\frac{22}{7}\).)

• A. 420 cm\(^2\)
• B. 440 cm\(^2\)
• C. 480 cm\(^2\)
• D. 220 cm\(^2\)

Hint:

Picture the curved surface of the cylinder unrolled flat - it becomes a rectangle whose sides are the base circumference and the cylinder's height.

Answer 1

The Correct Option is B

Step 1: Instead of applying the curved surface area formula in one shot, think of the cylinder's curved surface unrolled flat into a rectangle.
Step 2: When you cut the curved surface of a cylinder along its height and unroll it, you get a rectangle whose length equals the circumference of the circular base and whose width equals the height of the cylinder.
Step 3: Circumference of the base $=2\pi r=2\times\frac{22}{7}\times7=44$ cm.
Step 4: The unrolled rectangle has length $44$ cm and width $=$ height of cylinder $=10$ cm.
Step 5: Curved surface area $=$ area of this rectangle $=$ length $\times$ width $=44\times10=440$ cm$^2$. \[\boxed{440\ \text{cm}^2}\]