A cone has a radius of 15 cm and a volume of 540 cm3. What is the volume of a similar cone with a radius of 10 cm?
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height of the cone.
Since the two cones are similar, their corresponding dimensions are proportional. That is, if the radius of the first cone is 15 cm and its volume is 540 cm^3, and the radius of the second cone is 10 cm, then the ratio of their radii is 10/15 = 2/3.
To find the height of the second cone, we can use the fact that the ratio of the volumes of two similar cones is equal to the cube of the ratio of their corresponding dimensions. That is,
(Volume of second cone) / (Volume of first cone) = (10/15)^3
(Volume of second cone) / 540 = (2/3)^3
(Volume of second cone) = 540 x (8/27)
(Volume of second cone) = 160 cm^3
Therefore, the volume of the similar cone with a radius of 10 cm is 160 cm^3.