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 2m and 6m respectively and the slant height of the top is 2.4m. 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.300 per m²???

Answer 1

h=2 cm
d= 6cm
so, r=3cm
so, Curve surface area =2πrh
=2×22/7×3×2
=264/7cm^2
now, Lateral surface area of cone=πrl
= 22/7×3×2.4
=792/5cm^2
So, total s.a. of canvas =264/7+792/5
=1320+5544/35=
=6864/35cm^2
Hope this will help u

Answer 2

$\large\underline{Given:-}$

• Slant height of cone = 2.4 m
• Height and Diameter of cylinder = 2 m and 6 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 300 per m² ...?

$\large\underline{Solutions:-}$

• Diameter of the cone = 6 m
• Radius of the cone = 3 m
• Slant height of cone = 2.4 m

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

$\: \: \: \: \: \leadsto \: \: \frac{22}{7} \: \times \: {3} \: \times \: {2.4}$

$\: \: \: \: \: \leadsto \: \: \frac{158.4}{7}$

$\: \: \: \: \: \leadsto \: \: {22.62} \: {m}^{2}$

And,

• Diameter of cylinder = 6 m
• Radius of cylinder = 3 m
• Height of cylinder = 2 m

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

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: \frac{22}{7} \: \times \: {3} \: \times \: {2}$

$\: \: \: \: \: \leadsto \: \: \frac{264}{7}$

$\: \: \: \: \: \leadsto \: \: {37.71} \: {m}^{2}$

Area of the canvas used.

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

$\: \: \: \: \: \leadsto \: \: {22.62} \: + \: {37.71}$

$\: \: \: \: \: \leadsto \: \: {60.33} \: {m}^{2}$

The cost of the canvas of the tent at the rate of Rs. 300 per m².

$\: \: \: \: \: \leadsto \: \: {300} \: \times \: {60.33}$

$\: \: \: \: \: \leadsto \: \: {18,099}$

Hence, The area of the canvas required for the tent is 60.33 m²and The cost of the canvas of the tent at the rate of the Rs 300 per m² is 18,099.

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