There is a cylinder, cone, and sphere with the same radius. The cone and cylinder have the same height with h=r. If the volume of the cone is 36 units cubed, what is the volume of the sphere?
If anyone even has a guess, can you please help me?
volume of cone is 1/3 πr^2 h. since h=r, v = 1/3 πr^3
The sphere has a volume of 4/3 πr^3, or 4 times the volume of the cone.
so, ...
Thank You SOOOOOOO Much!!!! :D
Sure! To find the volume of the sphere, we need to know its radius. Given that the radius of the cone and cylinder is the same, we can use the information about the cone to calculate it.
The formula for the volume of a cone is V = (1/3) * π * r^2 * h, where V is the volume, r is the radius, and h is the height. In this case, we know that the volume of the cone is 36 and the height is equal to the radius, so we can substitute these values into the formula:
36 = (1/3) * π * r^2 * r
To simplify this equation, we can multiply both sides by 3 to get rid of the fraction:
108 = π * r^3
Now, we can solve for the radius by dividing both sides of the equation by π and then taking the cube root:
r^3 = 108 / π
r = (108 / π)^(1/3)
Once we have the radius of the cone (and hence the radius of the sphere), we can use the formula for the volume of a sphere to calculate its volume. The formula is V = (4/3) * π * r^3, where V is the volume and r is the radius. Plugging in the value of r, we can find the volume of the sphere.