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: Write the radius as a fraction to avoid decimals.
$R = 1.4\text{ m} = \frac{7}{5}\text{ m}$, so $R^2 = \frac{49}{25}$.
Step 2: Compute the curved surface area of the hemisphere using fractions.
$\text{CSA} = 2\pi R^2 = 2 \times \frac{22}{7} \times \frac{49}{25} = \frac{2 \times 22 \times 7}{25} = \frac{308}{25} = 12.32\text{ m}^2$.
Step 3: Subtract the door opening.
The actual outer fabric area is $12.32 - 0.50 = 11.82\text{ m}^2$.
\[ \boxed{11.82\text{ m}^2} \]