Sphere volume: [tex] \frac{4}{3} \pi r^3[/tex]
[tex] \frac{4}{3} \pi 6^3 [/tex]
[tex] \frac{4}{3}*216 \pi [/tex]
[tex]288 \pi [/tex]
V = 288π = 288*3,14 = 904,3 m³
Cone volume: [tex] \frac{ \pi r^2h}{3} [/tex]
We don't have the height, so we should find it firstly.
Watch the triangle "inside" the cone. It is a right triangle. The apothem is the hypothenuse and the radius is the shortest leg.
Apply Pitagora.
h (longest leg) = √13²-5² = √169-25 = √144 = 12 m
V = [tex] \frac{ 5^2*12 \pi}{3} [/tex]
[tex] \frac{25*12* \pi }{3} [/tex]
[tex] \frac{300 \pi }{3} [/tex]
(300*3,14)/3 = 942/3 = 314 m³
Parallelepiped volume: a*b*h
a = 11, b = 5, h = 6
V = 11*5*6 = 330 cm³
