Ice-cream, completely filled in a cylinder of diameter 35 cm and height 32 cm, is to be served by completely filling identical disposable cones of diameter 4 cm and height 7 cm. The maximum number of cones that can be used in this way is

We know the volume of a cylinder of radius $$r$$ and height $$h$$ is $$\pi r^2h$$

Given D = 35 cm, so $$r=17.5$$ cm

Also, $$h=32$$ cm

So, Volume = $$\pi r^2h=\pi\ \left(17.5\right)^2\times32\ cm^3$$

We know that the volume of a cone of radius $$r$$ and height $$h$$ is $$\dfrac{1}{3}\pi r^2h$$

Given the diameter of cone = 4 cm, so the radius = 2 cm

Height = 7 cm

So, the volume of the cone is $$\dfrac{1}{3}\pi r^2h=\dfrac{1}{3}\pi\left(2\right)^2\times7$$

To find the maximum number of cones that can be used, divide the volume of the cylinder by the volume of a cone

Max cones = $$\dfrac{\pi\left(17.5\right)^2\times32}{\dfrac{1}{3}\pi\left(2\right)^2\times7}=1050$$

Hence, the answer is 1050.