Question

The volume of a cone whose height h and base radius is r is given by the formula of the volume of a cone,express r in terms of v,pie and h and find the value of h when the volume of the cone is 660cm raise to power 3,where r is 14cm(pie=22/7)

Answer 1

The formula for the volume of a cone is:

V = (1/3)πr^2h

Solving for r:

V = (1/3)πr^2h

3V = πr^2h

r^2 = (3V)/(πh)

r = sqrt[(3V)/(πh)]

Given that V = 660cm^3, h = 14cm and π = 22/7:

r = sqrt[(3 × 660)/(22/7 × 14)] ≈ 7 cm

So the radius is approximately 7 cm.

To find the value of h:

V = (1/3)πr^2h

660 = (1/3)(22/7)(7^2)h

660 = (22/3)(49/7)h

660 = (22/3)(7)h

h = 660 / [(22/3)(7)]

h = 9.45 cm (rounded to two decimal places)

Therefore, the value of h when the volume of the cone is 660 cm^3 is approximately 9.45 cm.