Question

If the curved surface area of a hemisphere is 1232 cm\(^2\) then its radius is

• A. 7 cm
• B. 14 cm
• C. 21 cm
• D. 28 cm

Hint:

When solving for \(r^2\), try to break down the numbers into factors that are perfect squares before multiplying them out. This makes taking the square root much easier.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
We are given the curved surface area (CSA) of a hemisphere and need to find its radius. We can do this by using the formula for the CSA of a hemisphere and solving for the radius, \(r\).

Step 2: Key Formula or Approach:
The formula for the curved surface area of a hemisphere is:
\[ CSA = 2\pi r^2 \] We will substitute the given values and solve for \(r\).

Step 3: Detailed Explanation:
We are given CSA = 1232 cm\(^2\). Use \(\pi \approx \frac{22}{7}\).
\[ 1232 = 2 \times \frac{22}{7} \times r^2 \] \[ 1232 = \frac{44}{7} \times r^2 \] To isolate \(r^2\), multiply both sides by \(\frac{7}{44}\):
\[ r^2 = 1232 \times \frac{7}{44} \] Let's simplify the division. We can divide 1232 by 44. (Hint: 1232 / 44 = 1232 / (4 * 11) = 308 / 11 = 28).
\[ r^2 = 28 \times 7 \] \[ r^2 = (4 \times 7) \times 7 = 4 \times 49 \] Now, take the square root to find \(r\):
\[ r = \sqrt{4 \times 49} = \sqrt{4} \times \sqrt{49} = 2 \times 7 = 14 \] The radius is 14 cm.

Step 4: Final Answer:
The radius is 14 cm.