Thevolumeofthe 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 radiusofthe base circle and h is the heightofthecone.

Findtheheightofaconewithavolumeof 21 ft3 and a radiusof 4 ft. 7. Findtheradiusofaconewithavolumeof 175 cm 3 and a heightof 21 cm. 8. Findtheheightofaconewithavolumeof 150 in3 and a radiusof 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 volumeofthecone V= 31πr 2h The main objective to findthe rate of change of the volume w.r.t the radiusofthecone. 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 volumeofconewith respect to r.

The formula to findthevolumeofacone, 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 coneand h = heightofthecone. Therefore, the volumeofcone= (1/3) × A × h. Since the base of the cone is circular, we substitute the area to be πr 2.

Thevolumeoftheright circularconeis equal to one-third of the product of the area of the circular base and itsheight.Theformula for thevolumeis V = (1/3) × πr 2 h where r is theradiusofthebase circle and h is theheightofthecone.Findtheheightofaconewithavolumeof21 ft3 and aradiusof4 ft. 7.Findtheradiusofaconewithavolumeof175 cm 3 and aheightof21 cm. 8.Findtheheightofaconewithavolumeof150 in3 and aradiusof10 in. Missing Dimensions Practice: LT 6.5 9. A cylinder has aheightthat is 2 times as large as itsradius.volumeoftheconeV= 31πr 2h The main objective tofindtherate of change of thevolumew.r.t theradiusofthecone. 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 thevolumeofconewithrespect to r.Theformula tofindthevolumeofacone, whoseradiusis 'r' andheightis 'h' is givenas,Volume= (1/3) πr 2 h cubic units. Let A = Area of base of theconeandh =heightofthecone. Therefore, thevolumeofcone= (1/3) × A × h. Since the base of theconeis circular, we substitute the area to be πr 2.