Question

There are two water tanks atop a building, each of height 2 metres. One is a rectangular prism of base lengths 8 metres and 2 metres and the other is a square prism of base length 4 metres. What is the volume of each? What is the cost of painting the outer surface of each tank, at 250 rupees per square metre? Which costs less?

Answer 1

Length of the rectangular tank, l = 8 m

Breadth of the rectangular tank, b = 2 m

Height of the rectangular tank, h = 2 m

Each side of the base of the square tank, a = 4 m

Height of the square tank, h = 2 m

Volume of the rectangular tank = l × b × h

= 8 m × 2 m × 2 m

= 32 m³

Volume of the square tank = a × a × h

= 4 m × 4 m × 2 m

= 32 m³

Outer surface area of the rectangular tank = 2(bh + hl)

= 2 (2 × 2 + 2 × 8) m²

= 2(4 + 16) m²

= 2 × 20 m²

= 40 m²

Outer surface area of the square tank = 4ah

= 4 × 4 m × 2 m

= 32 m²

Cost of painting per square metre of the tank = Rs.250

∴ Cost of painting the outer surface area of the rectangular tank = Rs.250 × 40 = Rs.10000

Cost of painting the outer surface area of the square tank = Rs.250 × 32 = Rs.8000

Thus, the painting cost of the square tank is less than the painting cost of the rectangular tank.