Surface Area

Exercise 13.3 Part 2

Question 5: What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm (Use π = 3.14).

Answer: h = 8 m, r = 6 m
Here; `l^2 = h^2 + r^2`
`= 8^2 + 6^2`
`= 64 + 36 = 100`
Or, `l = 10  m`

CSA of cone `= π rl`
`= 3.14 xx 6 xx 10 = 188.4  sq  m`

Hence, required length of material `= (188.4/3) + 0.2  m`
`= 62.8 + 0.2 = 63  m`


Question 6: The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of white-washing its curved surface at the rate of Rs 210 per 100 m2.

Answer: l = 25 m, d = 14 m or, r = 7 m
CSA of cone `= π rl`
`= (22/7) xx 7 xx 25 = 550  sq  m`
`Co\st = Ar\ea\xx\ra\te`
`= 550 xx (210/100) = Rs. 1155`


Question 7: A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps.

Answer: r = 7 cm, h = 2 cm
Here; `l^2 = h^2 + r^2`
`= 24^2 + 7^2`
`= 576 + 49 = 625`
Or, `l = 25  cm`

CSA `= π rl`
`= (22/7) xx 7 xx 25 = 550  sq  cm`
Area of sheet for 10 caps `= 550 xx 10 = 5500  sq  cm`

Question 8: A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. If the outer side of each of the cones is to be painted and the cost of painting is Rs 12 per m2, what will be the cost of painting all these cones? (Use π = 3.14 and take ∠1.04 = 1.02)

Answer: d = 40 cm or, r = 20 cm, h = 1 m
Here; `l^2 = h^2 + r^2`
`= 1^2 + (0.2)^2`
`= 1 + 0.04 = 1.04`
Or, `l = sqrt1.04 = 1.02`

CSA of cone `= π rl`
`= 3.14 xx 1.02 xx 0.2`

CSA of 50 cones `= 3.14 xx 1.02 xx 0.2 xx 50`
`= 3.14 xx 1.02 xx 10 = 32.028`
`Co\st = Ar\ea\ xx Ra\te`
`= 32.028 xx 12 = Rs. 384.33`



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