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Surface Areas and Volumes
NCERT Exemplar Ch 11
CBSE_NCERT_EXEMPLAR_CH11
Grade 10

Question:

A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are $2.1\text{ m}$ and $4\text{ m}$ respectively, and the slant height of the top is $2.8\text{ m}$, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs $500$ per $\text{m}^2$. (Note that the base of the tent will not be covered with canvas).

Step-by-Step Solution

Key Concept: Area of canvas $= \text{CSA of cylinder} + \text{CSA of cone} = 2\pi r h + \pi r l = \pi r(2h + l)$.
Stepwise Solution:

Radius $r = 2\text{ m}$. Height of cylinder $h = 2.1\text{ m}$. Slant height of cone $l = 2.8\text{ m}$. [1.0 Mark]

CSA of cylinder $= 2 \pi r h = 2 \times \dfrac{22}{7} \times 2 \times 2.1 = 26.4\text{ m}^2$. [1.0 Mark]

CSA of cone $= \pi r l = \dfrac{22}{7} \times 2 \times 2.8 = 17.6\text{ m}^2$. [1.0 Mark]

Total area of canvas $= 26.4 + 17.6 = 44\text{ m}^2$. [1.0 Mark]

Cost of canvas $= 44 \times 500 = \text{Rs } 22000$. [1.0 Mark]

Marking Scheme:

• Identifying correct dimensions $r=2, h=2.1, l=2.8$: 1.0 Mark
• CSA of cylinder $= 26.4\text{ m}^2$: 1.0 Mark
• CSA of cone $= 17.6\text{ m}^2$: 1.0 Mark
• Total canvas area $= 44\text{ m}^2$: 1.0 Mark
• Calculating cost $=$ Rs 22,000: 1.0 Mark

Correct Answer:
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