a room is 9 m long. 8m wide and 4m high. find the cost of plastering its wall and ceiling at the rate of RS 250 per square metre
The dimensions of the room are
`l = 9 m, b = 8 m and h = 4 m `
To find the cost of plastering the walls and the ceiling we need to find the area of the four walls and the ceiling. The room is in cuboidal shape.
Total surface area of the room = `2(lb + bh + hl)`
But here we should not consider the floor of the room.
So, the required area is `lb + 2bh + 2hl`
Required area = `9*8 + 2(8*4) + 2(4*9)`
=`72 + 64 + 72 = 208 m^2 `
The cost of plastering per square meter = Rs 250
The cost of plastering for 208 square meter =`250 X 208 = Rs.52,000`
Each wall and the ceiling has rectangular shape. The area of a rectangle is its width multiplied by its length.
There are two walls with the dimensions 9 m and 4 m, two walls 8 m by 4 m and the ceiling 8 m by 9 m. Their total area is
2*8*4 + 2*9*4 + 8*9 = 4*(16 + 18 + 18) = 4*52 (square meters).
The cost is this area multiplied by the price for one square meter, i.e.
250*4*52 = 1000*52 = 52000 (RS). This is the answer.
l= 9 , b=8, h=4
Total Surface area of a the room S = 2lb + 2lh + 2bh = 2(lb + lh + bh)
Since only the balls are to be plastered
Total Surface Area - Area of the Top face
=(2lb + 2lh + 2bh) - lb
= lb + 2lh + 2bh
= 9*8 + 2*9*4 + 2*8*4
Cost of plastering = 208* 250
= Rs 52000
We want to cover the walls and ceiling with plaster. Since we understand that the measure of the space "inside" a shape is called area, we know we are looking for the area of the four walls and the ceiling. Each wall and the ceiling are rectangles, and the area of a rectangle is calculated by multiplying width times length: a = lw
Two of the walls are 9m by 4m: a = lw; a = (9)(4); a= 36 sq meters.
Two of the walls are 8m by 4m: a = lw; a = (8)(4); a = 32 sq meters.
The ceiling measures 9m by 8m: a = lw; a = (9)(8); a = 72 sq meters.
The total area we need to cover with plaster is 36 + 36 + 32 + 32 + 72 (all four walls and the ceiling). Total area is 208 sq meters.
The cost is 250 per square meter, so we just need to multiply our total square meters by the cost per square meter.
208 sq meters x Rs 250 = Rs 52,000.