# Surface Areas and Volumes

## Class 9 NCERT Maths

### NCERT

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:$\\$ (i) The area of the sheet required for making the box.$\\$ (ii) The cost of sheet for it, if a sheet measuring $1 m^2$ costs Rs. $20.$

It is given that, length (l) of box $= 1.5 m$$\\ Breadth (b) of box = 1.25 m$$\\$ Depth (h) of box $= 0.65 m$$\\ (i) Box is to be open at top.\\ Area of sheet required\\ = 2lh + 2bh + lb$$\\$ $= [2 * 1.5 * 0.65 + 2 * 1.25 * 0.65 + 1.5 * 1.25] m^2$$\\ = (1.95 + 1.625 + 1.875) m^2 = 5.45 m^2$$\\$ (ii) Cost of sheet per $m^2$ area = Rs. $20$$\\ Cost of sheet of 5.45 m^2 area = Rs. (5.45 * 20) = Rs. 109 2 The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of Rs. 7.50 per m^2 . ##### Solution : It is given that\\ Length (l) of room = 5 m$$\\$ Breadth (b) of room $= 4 m$$\\ Height (h) of room = 3 m$$\\$ It can be observed that four walls and the ceiling of the room are to be whitewashed. The floor of the room is not to be white-washed.$\\$ Area to be white-washed = Area of walls + Area of ceiling of room$\\$ $= 2lh + 2bh + lb$$\\ = [2 * 5 * 3 + 2 * 4 * 3 + 5 * 4] m^2$$\\$ $= (30 + 24 + 20) m^2$$\\ = 74 m^2$$\\$ Cost of white-washing per $m^2$ area = Rs. $7.50$$\\ Cost of white-washing 74 m^2 area = Rs. (74 × 7.50) = Rs. 555 3 The floor of a rectangular hall has a perimeter 250 m. If the cost of panting the four walls at the rate of Rs.10 per m^2 is Rs. 15000, find the height of the hall. [Hint: Area of the four walls = Lateral surface area.] ##### Solution : Let length, breadth, and height of the rectangular hall be l m, b m, and h m respectively.\\ Area of four walls = 2lh + 2bh = 2(l + b) h$$\\$ Perimeter of the floor of hall $= 2(l + b) = 250 m$$\\ \therefore Area of four walls = 2(l + b) h = 250h m^2$$\\$ Cost of painting per $m^2$ area = Rs. $10$$\\ Cost of painting 250h m^2 area = Rs. (250h × 10) = Rs. 2500h$$\\$ However, it is given that the cost of paining the walls is Rs. $15000.$$\\ \therefore 15000 = 2500h$$\\$ $h = 6$$\\ Therefore, the height of the hall is 6 m.$$\\$

4   The paint in a certain container is sufficient to paint an area equal to $9.375 m^2$ . How many bricks of dimensions $22.5 cm *10 cm * 7.5 cm$ can be painted out of this container?