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 ?

12800

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