Step-by-step explanation:
2. The storage container is in the shape of a right circular cylinder with a diameter of 15 in and 10 in high. A right circular cylinder is considered a cylinder with circular bases with the axis of the cylinder being perpendicular (forms [tex]90^{\circ}[/tex]) with the base.
The volume of a right circular cylinder is evaluated following the formula
[tex]V \ = \ \pi r^{2}h[/tex],
where [tex]V[/tex] denotes volume, [tex]r[/tex] is the radius of the circular base and [tex]h[/tex] is the height of the cylinder.
Plugging the given values into the formula and let [tex]\pi \ = \ 3.1415[/tex],
[tex]V \ = \ (3.1415)\left(\displaystyle\frac{15}{2}\right)^{2}(10) \\ \\ V \ = \ 1767.1 \ \ \text{in}^3 \ \ \ \ \ \ (\text{nearest tenth})[/tex].
3. The ball is the shape of the sphere in which the volume is determined by the formula
[tex]V \ = \ \displaystyle\frac{4}{3}\pi r ^{3}[/tex].
Therefore,
[tex]V \ = \ \displaystyle\frac{4}{3}(3.1415)\left(\displaystyle\frac{38}{2}\right)^{3} \\ \\ V \ = \ 28730.1 \ \text{cm}^{3} \ \ \ \ \ (\text{nearest tenth})[/tex]