A tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and the radius of the cylindrical part are 3m and 14m and height of conical part is 13.5m from the ground to the top. Find the cost of Canvas needed to make the tent if the Canvas is available at the rate of ₹ 4 per square metre.
WRONG ANSWERS WILL BE REPORTED
Share
Verified answer
Answer:
CSA of cylinder =2πrh
2 \times \frac{22}{7} \times 14 \times 3 \\ = 264 {m}^{2}
radius=14m
height =13.5-3=10.5
l {}^{2} = r {}^{2} + h {}^{2}
14 { }^{2} + 10.5 { }^{2} \\ 196 + 110.25 \\ = 306.25 \\ l \sqrt{306.25 } \\ l = 17.5m
CSA of cone =πrl
\frac{22}{7} \times 14 \times 17.5 \\ = 770 {m}^{2}
total area=264+770
1034 {m}^{2}
cost of cloth per square m = Rs80
cost of cloth
1034 {m}^{2}
80 \times 1034 \\ = 82720
Height (h) of the cylindrical part = 2.1 m
Diameter of the cylindrical part = 3 m
Radius of the cylindrical part = 3/2 m
Slant height (l) of conical part = 2.8 m
Total canvas used = CSA of conical part + CSA of cylindrical part
= πrl + 2πrh
= πr(2h+l)
= (22/7)×3/2(2×2.1+2.8)
= (22/7)×3/2(4.2+2.8)
= (22/7)×3/2(7)
= 11×3
= 33 m²
Cost of 1 m² canvas = ₹ 500
Cost of 44 m² canvas = 33 × 500 = 16500
The cost of Canvas needed to make the tent= ₹ 16500
Hence, it will cost ₹ 16500 for making such a tent.
[tex]\rule{200}{2}[/tex]