Respuesta :

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

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