Question

A cylinder has radius $7\text{ cm}$ and height $10\text{ cm}$. Find its curved surface area. [$\text{CSA} = 2\pi rh$]

• A. $220\text{ cm}^2$
• B. $440\text{ cm}^2$
• C. $560\text{ cm}^2$
• D. $770\text{ cm}^2$

Hint:

When the radius is a multiple of 7, always use $\pi = \frac{22}{7}$ instead of $3.14$ to make the calculation much faster and cleaner!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The question belongs to the field of Mensuration, specifically dealing with three-dimensional geometric solids.
A cylinder is defined as a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a fixed plane curve in a plane not parallel to the given line.
In simple terms, a right circular cylinder has two parallel circular bases and a curved side.
The Curved Surface Area (CSA) represents the area of this side surface only, excluding the top and bottom circles.
Calculating the CSA is essential in various engineering and manufacturing contexts, such as determining the amount of metal required for a pipe or the area to be painted on a pillar.
Key Formula or Approach:
The standard formula for the Curved Surface Area of a cylinder is:
\[ CSA = 2\pi rh \]
Where:
\( r \) is the radius of the circular base.
\( h \) is the height of the cylinder.
\( \pi \) is a mathematical constant, approximately \(\frac{22}{7}\) or 3.14159.
Step 2: Detailed Explanation:
Let's analyze the given parameters from the question:
The radius (\( r \)) is provided as 7 cm.
The height (\( h \)) is provided as 10 cm.
Since the radius is exactly 7, it is mathematically convenient to use the fractional value of \( \pi = \frac{22}{7} \) because it will allow for direct cancellation, simplifying the arithmetic significantly.
Substitute the values into the formula:
\[ CSA = 2 \times \frac{22}{7} \times 7 \times 10 \]
First, we look at the interaction between the fraction and the radius:
\[ \frac{22}{7} \times 7 = 22 \]
The 7 in the numerator and the 7 in the denominator cancel each other out.
Now the expression simplifies to:
\[ CSA = 2 \times 22 \times 10 \]
Performing the multiplication step-by-step:
Multiplying 2 by 22 gives us 44.
Then, multiplying 44 by the remaining height factor of 10:
\[ 44 \times 10 = 440 \]
It is important to consider the units. Since radius and height are in centimeters (cm), the area must be in square centimeters (cm$^2$).
The final result is 440 cm$^2$.
Step 3: Final Answer:
The Curved Surface Area of the given cylinder is calculated to be 440 cm$^2$.
Comparing this result with the provided options, it matches exactly with Option (B).