Sarah is filling a glass sphere with decorative sand. The radius of the sphere is 2 inches. Which is closest to the minimum amount of sand Sarah needs to completely fill the glass sphere?
If she's filling up a sphere with sand, it means that we need to know what the volume of the sphere is. The formula for the volume of a sphere is:
(4π)*((r^3)/3))
We know that the radius is 2, so we have:
(4π)*((2^3)/3))
Now just simplify it.
To calculate the minimum amount of sand needed to fill the glass sphere, we can use the formula for the volume of a sphere which is V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.
In this case, the radius of the sphere is given as 2 inches. We can substitute this value into the formula to find the volume:
V = (4/3)π(2^3)
= (4/3)π(8)
= (32/3)π
The value of π (pi) is approximately 3.14159. Let's substitute this value to get an approximate answer:
V ≈ (32/3)(3.14159)
≈ 33.51033
Hence, the minimum amount of sand Sarah needs to completely fill the glass sphere is approximately 33.51033 cubic inches.