Exercise 13.1 Part 1
Question 1: A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet, determine:
- The area of the sheet required for making the box.
- The cost of sheet for it, if a sheet measuring 1m2 costs Rs 20.
Answer: l = 1.5 m, b = 1.25 m, h = 0.65 m
Area of base `= lxxb = 1.5xx1.25 = 1.875 sq m`
Area of four walls `=2h(l + b)=2xx0.65(1.5 + 1.25)=1.3xx2.75 = 3.575 sq m`
Total area `= 1.875 + 3.575 = 5.45 sq m`
`Co\st\=Ra\te\xxAr\ea\= 20xx5.45 = Rs. 109`
Question 2: The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs 7.50 per m2
Answer: l = 5m , b = 4m, h = 3 m, rate = Rs. 7.50 per sq m
Area of roof `= lxxb = 5xx4 = 20 sq m`
Area of four walls `= 2h(l + b)= 2xx3(5 + 4)=6xx9 = 54 sq m`
Total area `= 20 + 54 = 74 sq m`
`Co\st = Ra\te\xx\Ar\ea\ = 7.50xx74 = Rs. 555`
Question 3: The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of Rs 10 per m2 is Rs 15000, find the height of the hall. [Hint : Area of the four walls = Lateral surface area.]
Answer: Perimeter = 250m, rate = Rs. 10 per sq m, cost = Rs. 15000, h = ?
`Ar\ea\ = (co\st)/(ra\te)= 1500/10 = 1500 sq m`
Area of four walls `= hxxperimeter`
Or, `1500 = hxx250`
Or, `h = 1500/250 = 6 m`