Find the volume of a sphere with a radius of 4 ft
1. 33.5 ft3
2. 67.0 ft3
3. 267.9 ft3
4. 803.8 ft3
The correct answer is 4. 803.8 ft3
Explanation: The formula for the volume of a sphere is V = (4/3)πr^3. Plugging in the given radius of 4 ft, we get V = (4/3)π(4^3) = 803.8 ft3 (rounded to one decimal place).
explain why
The formula for the volume of a sphere is derived from calculus. But in simpler terms, we can think of a sphere as a set of infinitely many infinitesimal slices stacked on top of each other, each of which is a circular disk. The volume of each slice can be approximated by multiplying its circular area (πr^2) by its thickness (which is approximated as dr, an infinitesimal change in radius).
The total volume of the sphere is then obtained by adding up the volumes of all these infinitely many slices using calculus integration. This leads to the formula V = (4/3)πr^3, where r is the radius of the sphere.
Plugging in the given radius of 4 ft, we get V = (4/3)π(4^3) = 803.8 ft3, which is the volume of the sphere with a radius of 4 ft.
To find the volume of a sphere, we can use the formula:
V = (4/3) * π * r^3
where V is the volume and r is the radius.
Substituting the given values, we have:
V = (4/3) * π * (4 ft)^3
Simplifying further:
V = (4/3) * π * 64 ft^3
V = (4/3) * 3.1416 * 64 ft^3
V ≈ 267.9 ft^3
Therefore, the correct answer is option 3: 267.9 ft^3.