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 m and 4 m respectively, and the slant height of the top is 2.8 m.find the area of the canvas of the tent at the rate of Rs.500 per square m.​

Answer 1

Answer:

44m²

Step-by-step explanation:

Given:  

Height (h) of the cylindrical part = 2.1 m

Diameter of the cylindrical part = 4 m

Radius of the cylindrical part = 2 m

Slant height (l) of conical part = 2.8 m

Area of canvas used = CSA of conical part + CSA of cylindrical part

                             =πrl+2πrh

                             =π×2×2.8+2π×2×2.1

                             =2π[2.8+4.2]

                             =2×7 ×22/7 =44m  2 Cost of 1 m  

canvas =500 rupees

Cost of 44 m  

2 canvas =44×500=22000 rupees.

Therefore, it will cost 22000 rupees for making such a tent.

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Answer 2

$\large\underline{Given:-}$

• Slant height of cone = 2.8m
• Height and Diameter of cylinder = 2.1 m and 4 m.

$\large\underline{To find:-}$

• find the area of the canvas required for the tent ...?
• The cost of the canvas of the tent at the rate of the Rs 500 per m² ...?

$\large\underline{Solutions:-}$

• Diameter of the cone = 4 m
• Radius of the cone = 2 m
• Slant height of cone = 2.8 m

$\: \: \: \: \: \therefore \: \: Curved \: \: surface \: \: area \: \: = \: \: \pi \: r \: l$

$\: \: \: \: \: \leadsto \: \: \frac{22}{7} \: \times \: {2} \: \times \: {2.8}$

$\: \: \: \: \: \leadsto \: \: {22} \: \times \: {2} \: \times \: {0.4}$

$\: \: \: \: \: \leadsto \: \: {17.6} \: {m}^{2}$

And,

• Diameter of cylinder = 4 m
• Radius of cylinder = 2 m
• Height of cylinder = 2.1 m

$\: \: \: \: \: \therefore \: \: Curved \: \: area \: \: of \: \: cylinder \: \: = \: \: {2} \: \pi \: r \: h$

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: \frac{22}{7} \: \times \: {2} \: \times \: {2.1}$

$\: \: \: \: \: \leadsto \: \: \frac{{22} \: \times \: {2} \: \times \: {2} \: \times \: {21}}{{7} \: \times \: {10}}$

$\: \: \: \: \: \leadsto \: \: \frac{132}{5}$

$\: \: \: \: \: \leadsto \: \: {26.4} \: {m}^{2}$

Area of the canvas used.

$\: \: \: \: \: \therefore \: \: CSA \: \: of \: \: cone \: + \: CSA \: \: of \: \: cylinder$

$\: \: \: \: \: \leadsto \: \: {17.6} \: + \: {26.4}$

$\: \: \: \: \: \leadsto \: \: {44} \: {m}^{2}$

The cost of the canvas of the tent at the rate of Rs. 500 per m².

$\: \: \: \: \: \leadsto \: \: {500} \: \times \: {44}$

$\: \: \: \: \: \leadsto \: \: {22,000}$

Hence, the area of the canvas required for the tent is 44 m²and The cost of the canvas of the tent at the rate of the Rs 500 per m² is 22,000.

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