Answer:
Cone: 100ft^3
Sphere: 200ft^2
Step-by-step explanation:
Firstly, the volume of a cone is 1/3 of the volume of the cylinder. It's literally in the formula:
[tex]V_{cone} = \frac{h \pi r^2}{3}\\\textrm{As you can notice, }\pi r^2\textrm{ is the area of the base, like in the cylinder formula}\\[/tex]
So we can just instantly tell that the volume of the cone is 100feet^3.
Not for the sphere - we can assume that if the height is the same, it's equal to two radiuses, or simply - to the diameter. Let's use the formula for the volume of a sphere, but substitute one of the radiuses with [tex]\frac{h}{2}[/tex]
[tex]V_{sphere} = \frac{4\pi r^3}{3} = \frac{2\pi r^2 h}{3} = \frac{2h\pi r^2}{3} = 2\cdot V_{cone}[/tex]
So we can instantly tell that the volume of the sphere is 200feet^3
