A candy company makes chocolate in the shape of solid cones. The original machine for making these chocolates

These chocolates processed chocolate at the rate of 100 kg per hour. The individual chocolate measured 1.5 cm across the base and 2 cm high. Now three new machines are being installed to make three other sizes, listed below. the three new machines will all produce the same number of pieces per hour as the original machine. But they will process chocolate at different rates, because the cones have different volumes. How much chocolate will each new machine process per hour?
A. Diameter 2.0cm Height 8.0cm
B. Diameter 2.5 Height 3.5
C. Diameter 3.5 Height 3.5

The volume of a cone is (π/3) r^2 h = (π/12) d^2 h, but since we only care about ratios, we can ignore the constants.

For the original machine, d^2 h = 2 • (3/2)^2 = 9/2, and it processes 100 kg of chocolate.

For any other machine, x/v = 100/(9/2) ==> x = 200v/9 where v = d^2 h for the other machine, and x is the number of kilograms of chocolate processed per hour.

Machine A: v = 8 • 2^2 = 32 ==> x = 200 • 32/9 = 711 kg/hr (Answer)

Machine B: v = (7/2)(5/2)^2 = 175/8 ==> x = (200/9)(175/8) = 486 kg/hr (Answer)

Machine C: v = (7/2)^3 = 343/8 ==> x = (200/9)(343/8) = 953 kg/hr (Answer)

Volume is proportional to diameter squared times height, so you can use ratios to find the new answers.

A 100kg/hr x (2.0^2 x 8.0) / (1.5^2 x 2.0) = 711.11 kg/hr
B 100kg/hr x (2.5^2 x 3.5) / (1.5^2 x 2.0) = 486.11 kg/hr
C 100kg/hr x (3.5^2 x 3.5) / (1.5^2 x 2.0) = 952.78 kg/hr