Question 7

We need to find the total curved surface area of the tent to determine the canvas required, then calculate its cost.

Step 1 — Identify dimensions

Let's list the given dimensions. The height of the cylindrical part is $h_c = \textbf{2.1 m}$. The diameter of the cylindrical part is $\textbf{4 m}$. We can find the radius from the diameter. Radius $r = \text{diameter} / 2$.

$r = 4 \text{ m} / 2$ $= 2 \text{ m}$

The slant height of the conical top is $l = \textbf{2.8 m}$. The radius of the conical part is the same as the cylindrical part.

$\boxed{\text{Radius } r = 2 \text{ m}}$

Step 2 — Calculate the area of canvas

The tent's base is not covered. We need the curved surface area of the cylinder. We also need the curved surface area of the cone. The total canvas area is the sum of these two areas. CSA of a cylinder = $2\pi r h_c$. CSA of a cone = $\pi r l$.

$\text{Total Area} = 2\pi r h_c + \pi r l$ $= \pi r (2h_c + l)$ Let's substitute the values. We will use $\pi = 22/7$.

$\text{Total Area} = \frac{22}{7} \times 2 \times (2 \times 2.1 + 2.8)$ $= \frac{22}{7} \times 2 \times (4.2 + 2.8)$ $= \frac{22}{7} \times 2 \times 7$ $= 22 \times 2$

$\boxed{44 \text{ m}^2}$

Step 3 — Calculate the cost of canvas

The cost of canvas is ₹500 per square meter. We have calculated the total area of canvas needed. Let's multiply the area by the rate.

$\text{Cost} = \text{Total Area} \times \text{Rate}$ $= 44 \text{ m}^2 \times ₹500/\text{m}^2$ $= 44 \times 500$ $= 22,000$

$\boxed{₹22,000}$

Answer

(i) The area of the canvas used for making the tent is $44 \text{ m}^2$. (ii) The cost of the canvas of the tent is ₹$22,000$.