We can find the volume of a sphere with the formula:
[tex]V=\frac{4}{3}\pi r^3[/tex]1) When the radius of the sphere is r=7 in, the volume V is:
[tex]V=\frac{4}{3}\pi(7)^3=\frac{4}{3}\pi\cdot343=\frac{1372}{3}\pi[/tex]2) When the diameter of the sphere is d=33 in, the radius is r=33/2 and the volume V is:
[tex]V=\frac{4}{3}\pi(\frac{33}{2})^3=\frac{4}{3}\pi\cdot\frac{35937}{8}=\frac{1}{3}\cdot\frac{35937}{2}\cdot\pi=\frac{17968.5}{3}\pi[/tex]3) The surface area of a sphere can be calculated with the formula:
[tex]A=4\pi r^2[/tex]Then, if the sphere has a radius r = 2.8 in, the area A is:
[tex]A=4\pi(2.8)^2=4\pi\cdot7.84=31.36\pi[/tex]4) In this case we know that the diameter is D = 24 mm, so the radius is r = 12 mm.
Then, the area is:
[tex]A=4\pi(12)^2=4\pi\cdot144=576\pi[/tex]Answer:
1) (1372/3) π
2) (17968.5/3) π
3) 31.36π
4) 576π
