Question

the cost of circular mirrors is directly proportional to the square of the diameter. a circular mirror with a diameter of 60cm costs £50. What is the cost of a circular mirror with a diameter of 90cm?

Answer 1

When 'y' is directly proportional to 'x', we express this by

y = kx

where 'k' is the constant, which we need to work out first

Cost of circular mirrors = (k) (diameter)²
50 = k(60)²
50 ÷ 3600 = k 

the proportional formula is

y = (1/72)x²

The cost of the mirror when diameter = 90cm

y = (1/72) (90)²
y = 112.5

Answer: $112.50