What is the value of x if the volume of the cone is 12π m3 ?
(1 point)
4 m
4 m
5 m
5 m
6 m
6 m
10 m
The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone.
If we plug in the volume (V = 12π m^3) into the formula and solve for r and h, we get:
12π = (1/3)πr^2h
Multiplying both sides by 3 to get rid of the fraction gives:
36 = r^2h
We also know that the volume of the cone is given by V = (1/3)πr^2h, so we can rewrite the formula as:
12π = (1/3)πr^2h
Dividing both sides by π gives:
12 = (1/3)r^2h
Substitute in r^2h:
r^2h = 36
Now we can find the value of r if we know the value of h. Let's try to find out the value of h:
h = 36 / r^2
Given the values that r will be half of h:
r = h / 2
So if we substitute r = h / 2 in r = 36 / r^2, we can solve for h:
h / 2 = 36 / (h / 2)^2
Multiplying both sides by 2 to get rid of the fraction on the left side:
h = 72 / h
Therefore, the value of h that satisfies this equation is 6 m.
By substituting h = 6 m in r = h / 2, we get:
r = 6 m / 2 = 3 m.
Thus, the value of x is 6 m.