The director of the department of transportation wants to know if the pile of salt for use on the ice roads is too tall to cover with their tarpaulin. The salt is in a pile that is shaped like a right circular cone. The formula for the volume of a right circular cone is v = 1/3 (pie r squared h). The radius, r, of the circular base of the pile is 2.5 meters. The volume of the cone, V, is 40 cubic meters. If the tarpaulin can cover a cone up to 7 meters tall, can it cover the pile?

Yes! The tarpaulin can cover a cone up to 7 meters tall. Use the formula to calculate the volume of a cone this tall. (We must assume the tarpaulin is shaped like a right circular cone) If the calculated volume is greater than the 40 cubic meters of the salt pile, then we know the salt pile will fit under the tarpaulin. The tarpaulin's volume is V = 1/3 pi r**2 h = 1/3 * 3.14 * 2.5 * 2.5 * 7 (all dimensions in meters) = 45.79 cubic meters. Since the tarpaulin's volume of 45 is greater than the actual volume ( = 40) of the salt pile, we know the salt pile will fit under the tarpaulin.