A solid wax right cone is melted and a number of right cylinder are made with the material find then the number of cylinders of the radius of the base of each cylinder is $\displaystyle \frac{1}{3}$ rd the radius of the cone and the height of each cylinder is half the height of cone

The volumes remain constant during melting, so the volume of the cone equals the total volume of all cylinders using (1/3 * pi * R^2 * H) = N * (pi * r^2 * h). Substituting the given proportions r = R/3 and h = H/2 gives (1/3 * pi * R^2 * H) = N * (pi * (R/3)^2 * (H/2)). Simplifying the right side yields N * (pi * R^2 * H / 18), so equating the two sides means 1/3 = N/18, proving N is 6.

• Thanks
• Wrong explanation