The volume of a wall whose height is 10 times its width and whose length is 8 times its height is 51.2 m3. What is the cost(in ₹) of painting the wall on one side at the rate of ₹100/ m2 ?
Answer & explanation
Correct answer: option 1
We know that,
Volume = Length × Width × Height
Surface area of one side of a wall = Height × Length
We have,
The volume of the wall = 51.2m3
Height = 10 × Width
Length = 8 × Height
Let the width of the wall = x meter
Now,
Height = 10 × x = 10x meter
The measure of length = 8 × 10x = 80x meter
Now, The volume of the wall = x × 10x × 80x = 800x3 m3
According to the question,
800x3 = 51.2
= 8000 × x3 = 512
= x3 = 0.064
= x = 0.4
Now,
Width = 0.4m
Height = 0.4 × 10 = 4m
Length = 4 × 8 = 32m
Now, the surface area of one side of the wall = (4 × 32) = 128 m2
Cost of painting = Painting Cost per m2 × Surface area
The cost of painting the wall on one side = 128 × 100 = Rs. 12800