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: Understanding the Question:
We are given a camping tent shaped as a hemisphere with a radius $R = 1.4\text{ m}$.
The tent has a door opening of area $0.50\text{ m}^2$.
We need to find the actual outer surface area of the tent fabric, which is the total curved surface area of the hemisphere minus the area of the door opening.

Step 2: Key Formula or Approach:
The curved surface area (CSA) of a hemisphere of radius $R$ is given by:
\[ \text{CSA} = 2\pi R^2 \]
The net outer surface area of the fabric is:
\[ \text{Net Area} = \text{CSA of hemisphere} - \text{Area of door opening} \]

Step 3: Detailed Explanation:

• Identify the given parameters:
Radius of the hemispherical tent, $R = 1.4\text{ m}$
Area of the door opening $= 0.50\text{ m}^2$

• Calculate the curved surface area of the hemisphere:
\[ \text{CSA} = 2\pi R^2 \]
Substitute $\pi = \frac{22}{7}$ and $R = 1.4$:
\[ \text{CSA} = 2 \times \frac{22}{7} \times (1.4)^2 \]
\[ \text{CSA} = 2 \times \frac{22}{7} \times 1.96 \]
\[ \text{CSA} = 44 \times 0.28 \]
\[ \text{CSA} = 12.32\text{ m}^2 \]

• Calculate the actual outer fabric surface area of the tent by subtracting the door opening area:
\[ \text{Outer Surface Area} = 12.32\text{ m}^2 - 0.50\text{ m}^2 \]
\[ \text{Outer Surface Area} = 11.82\text{ m}^2 \]


Step 4: Final Answer:
The outer surface area of the tent is $11.82\text{ m}^2$.