Solution of 1st exercise chapter surface area and volume of class 9 NCERT book

Q.1. A piastic 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 :

i) The area of the sheet required for making the box.
(ii)The cost of sheet for it, if a sheet measuring 1 m cost Rs 20.
Sol.

 Here, length - 1.5 m, Breadth- 1.25 m, Height - 65 cm - 0.65 m.

Since the box is open at the top, it has only five faces.
(i) So, surface area of the box - Ib + 2(bh + hl)
1.5 x 1.25 m? + 2 (1.25 x 0.65 + 0.65 x 1.5) m^2
= 1.875 + 2 (1.7875) m^2
= (1.875 + 3.575) m2 - 5.45 m^2
Hence, 5.45 m^2of sheet is required Ans.
(ii) Cost of 1 m^2of the sheet = Rs 20
. cost of 5.15 m^2 of the sheet = Rs 20 x 5.15 m^2 = Rs 109 Ans.
Q.2. The length, hreadth and height of a room are 5 m,3 m and 3m. respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs 37.50 per m^2.
Sol. Here, l = 5 m, b = 4 m, h = 3 m
Surface area of the walls of the room and the ceilling
= 2h (l + b) + lb
= [2 x 3 (5 + 4) + 5 x 4] 12
= (6 x 9 + 20) m^2 - 74 m^2
Cost of white washing = Rs 7.50 per m^2
. total cost of white washing the walls and the ceilling of the room
= Rs 74 x 7.50 = Rs 555 Ans.

Q.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 m^2 is Rs 15000, find the height of the hall.

Sol. 

Let length, breadth and height of the hall be l, b and h respectively.

Perimeter of the floor of the hall = 2 ( l+ b)

= 250 m.

Area of the four walls of the hall = 2h (l + b)

.......(i)

Also, area of the four walls of the hall

15000m²÷10

= 1500 m².......(ii)

From (i) and (ii), we have

2h (l + b)= 1500

 h =1500÷250.                     [:: 2(1 + b) = 250]

= 6

Hence, height of the hall is 6 m Ans.