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An artist created the sculpture shown with concrete. The radius of the bottom hemisphere is double that of the top hemisphere. Find the exact total volume of concrete used for the sculpture if R equals 12 feet.

An artist created the sculpture shown with concrete The radius of the bottom hemisphere is double that of the top hemisphere Find the exact total volume of conc class=

Respuesta :

kishonwinston

Answer:

Vt = 4071.5 ft^3

Step-by-step explanation:

Givens:

  • R = 12
  • R = 2r => r = 6

Equations

  1. V = (4/3)(pi)r^3

Find: Vt (Total Volume)

Vt = (1/2)V1 + (1/2)(V2)

Vt = (1/2)(V1 + V2)                 [Factor out (4/3) and (pi) from volumes]

Vt = (1/2)(4/3)(pi)(R^3 + r^3)  [Sub in Values]

Vt = 4071.5 ft^3

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