The base diameter of a cone is 14cm, and its volume is 462 cm3. Find its height. [Taken \(\pi = \frac{22}{7}\)]

The base diameter of a cone is 14cm, and its volume is 462 cm³. Find its height. [Taken \(\pi = \frac{22}{7}\)]

Answer Details

The formula for the volume of a cone is given by V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. Since we are given the base diameter, which is 14cm, we can find the radius by dividing it by 2: radius, r = 14/2 = 7cm Also, we are given the volume of the cone, which is 462 cm^3. Substituting these values into the formula for the volume of a cone, we get: 462 = (1/3)π(7^2)h Simplifying this equation, we get: 22h = 198 h = 198/22 h = 9cm Therefore, the height of the cone is 9cm. Hence, the correct option is (d) 9cm.