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For a party, three solid cheese balls with diameters of 2 inches, 4 inches, and 6 inches, respectively, were combined to form a single cheese ball. what was the approximate diameter, in inches, of the new cheese ball? (the volume of a sphere is 43πr3,

Respuesta :

carlosego
The first thing we must do for this case is to define the volume of a sphere.
 We have then:
 [tex]V = \frac{4}{3} * (\pi) * (r ^ 3) [/tex]
 Where,
 r: sphere radio
 We look for the total volume of cheese balls.
 We have then:
 [tex]Vt = \frac{4}{3} * (\pi) * (( \frac{2}{2} ) ^ 3 + (\frac{4}{2})^3 + (\frac{6}{2})^3) [/tex]
 [tex]Vt = (4/3) * (\pi) * ((1) ^ 3 + (2) ^ 3 + (3) ^ 3) Vt = (4/3) * (\pi) * (1 + 8 + 27) Vt = 48 (\pi)[/tex]
 Then, Rewriting the left side of the equation we have: 
 [tex] \frac{4}{3} * (\pi) * (r ^ 3) = 48 (\pi) [/tex]
 Clearing the radio we have:
 [tex]r ^ 3 = \frac{3}{4} * (48) [/tex]
 [tex]r ^ 3 = 36[/tex]
 [tex]r = (36) ^ {(1/3)} [/tex]
 [tex]r = 3.3 inches[/tex]
 Then, the diameter will be:
 [tex]d = 2 * 3.3 d = 6.6 inches[/tex]
 Answer:
 The approximate diameter, in inches, of the new cheese ball is:
 [tex]d = 6.6 inches[/tex]