Surface Area

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:

  1. The area of the sheet required for making the box.
  2. 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 `=l\xx\b=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

Cost = Rate × Area `=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 `=l\xx\b=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

Cost = Rate × Area `=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 = ?

Area = Cost ÷ Rate `=(1500)/(10)=1500` sq m

Area of four walls = height × perimeter

Or, `1500=h\xx250`

Or, `h=(1500)/(250)=6` m

Question 4: The paint in a certain container is sufficient to paint an area equal to 9.375 m2. How many bricks of dimensions 22.5 cm × 10 cm × 7.5 cm can be painted out of this container?

Answer: l = 22.5 cm, b = 10 cm, h = 7.5 cm, total area = 9.375 sq m = 93750 sq cm

Surface area of brick `=2(lb+bh+lh)`

`=2(22.5xx10+10xx7.5+22.5xx7.5)`

`=2(225+75+168.75)`

`=2xx468.75=937.50` sq cm

Hence, number of bricks `= 93750/937.50 = 100`



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