Question

A camping tent in hemispherical shape of radius $1.4\text{ m}$, has a door opening of area $0.50\text{ m}^2$. Outer surface area of the tent is

• A. $11.78\text{ m}^2$
• B. $12.32\text{ m}^2$
• C. $11.82\text{ m}^2$
• D. $12.86\text{ m}^2$

Hint:

Be careful to read the question details completely.
The question mentions a door opening; failing to subtract the door area would lead to the incorrect option of $12.32\text{ m}^2$.

Answer 1

The Correct Option is C

Step 1: Recall what "outer surface" of the tent fabric means.
The fabric covers the curved hemisphere except where the door opening is cut out, so we need CSA of hemisphere minus the door area.
Step 2: Compute the full curved surface area first.
\[ \text{CSA} = 2\pi R^2 = 2 \times \frac{22}{7} \times 1.4 \times 1.4 \]
Since $1.4 \times 1.4 = 1.96$,
\[ \text{CSA} = \frac{44}{7} \times 1.96 = 44 \times 0.28 = 12.32\text{ m}^2 \]
Step 3: Subtract the door opening.
\[ \text{Outer area} = 12.32 - 0.50 = 11.82\text{ m}^2 \]
Step 4: Match with the options.
This is option (3), not the tempting but incomplete $12.32\text{ m}^2$.
\[ \boxed{11.82\text{ m}^2} \]