The volume of the right circular cone is equal to one-third of the product of the area of the circular base and its height. The formula for the volume is V = (1/3) × πr 2 h where r is the radius of the base circle and h is the height of the cone.
Find the height of a cone with a volume of 21 ft3 and a radius of 4 ft. 7. Find the radius of a cone with a volume of 175 cm 3 and a height of 21 cm. 8. Find the height of a cone with a volume of 150 in3 and a radius of 10 in. Missing Dimensions Practice: LT 6.5 9. A cylinder has a height that is 2 times as large as its radius.
Solution Verified by Toppr we know that the volume of the cone V= 31πr 2h The main objective to find the rate of change of the volume w.r.t the radius of the cone. So, differentiate with respect to r drdv= drd[31πr 2h] = 31πh[drd×r 2] = 31πh×2r = 32πrh Hence, this is the rate of change of the volume of cone with respect to r.
The formula to find the volume of a cone, whose radius is 'r' and height is 'h' is given as, Volume = (1/3) πr 2 h cubic units. Let A = Area of base of the cone and h = height of the cone. Therefore, the volume of cone= (1/3) × A × h. Since the base of the cone is circular, we substitute the area to be πr 2.