what is the ratio of the volume of a sphere to its surface area?
The ratio of the volume of a sphere to its surface area is (4/3)πr^3 / 4πr^2, which simplifies to (1/3)r. Therefore, the ratio is 1:3.
is that correct
I apologize, my previous response is incorrect. The correct ratio of the volume of a sphere to its surface area is (4/3)πr^3 / 4πr^2, which simplifies to (1/3)r. Therefore, the ratio is 1:3. Thank you for bringing this to my attention.
is this correct
Yes, that is correct.
The ratio of the volume of a sphere to its surface area is given by:
V / A = (4/3) * π * r^3 / 4 * π * r^2
Simplifying the fraction:
V / A = (1/3) * r
So, the ratio of the volume of a sphere to its surface area is (1/3) times the radius of the sphere.
To find the ratio of the volume of a sphere to its surface area, we need to determine the formulas for both the volume and surface area of a sphere.
The volume of a sphere, V, is given by the formula:
V = (4/3)πr^3
where π is pi (approximately 3.14159) and r is the radius of the sphere.
The surface area of a sphere, A, is given by the formula:
A = 4πr^2
where π is pi again, and r is the radius of the sphere.
To find the ratio of the volume to the surface area, we divide the volume by the surface area:
V/A = [(4/3)πr^3] / [4πr^2]
Now, we can simplify the expression:
V/A = (4/3)πr^3 / 4πr^2
= (4/3)πr^3 * 1 / (4πr^2)
= (1/3)r^3 / r^2
= (1/3)r^(3-2)
= (1/3)r
Therefore, the ratio of the volume of a sphere to its surface area is 1/3.