Find the approximate surface-area-to-volume ratio of a bowling ball with a radius of 5 inches.
A.
0.6
B.
0.67
C.
1.67
D.
25
surface area = 4πr^2
Volume = 4πr^3/3
S/V ratio = 4πr^2 / (4πr^3/3)
= 3/r
1.67
To find the surface-area-to-volume ratio of a bowling ball, you need to calculate its surface area and volume.
The surface area of a sphere can be found using the formula:
Surface Area = 4πr^2
Where r is the radius of the sphere.
In this case, the radius of the bowling ball is given as 5 inches, so we can substitute this value into the formula:
Surface Area = 4π(5)^2
= 4π(25)
= 100π
Next, we need to calculate the volume of the sphere. The volume of a sphere can be found using the formula:
Volume = (4/3)πr^3
Again, substituting the given radius:
Volume = (4/3)π(5)^3
= (4/3)π(125)
= (500/3)π
Now, to find the surface-area-to-volume ratio, divide the surface area by the volume:
Surface-area-to-volume ratio = Surface Area / Volume
Surface-area-to-volume ratio = (100π) / (500/3)π
= (100/1) / (500/3)
= 100 * (3/500)
= 3/5
So, the approximate surface-area-to-volume ratio of the bowling ball with a radius of 5 inches is 3/5.
None of the given answer choices match this result. Therefore, there seems to be a mistake in the answer choices provided.