Question

What is the volume of a sphere with a radius of 7mm

Answer 1

1) The answer, in terms of "π", is:
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" (
`(1372 mm^3)/(3)`) * π mm³ " .
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2) The answer, using "3.14" for "π", is:
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" 1436.0266666666666667 mm³ " ; round to: " 1436.027 mm³ " ;

or; write as: " 1436
`(2)/(75)` mm³ " .
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Explanation:
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The formula for the volume, "V" of a sphere is:

V =
`(4)/(3)` * π* r³ ;

in which "r" = radius = "7 mm" {given}.

We can solve using "3.14" for "π" ; or we can solve in terms of "π" ;
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1) In terms of "π" :
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V =
`(4)/(3)` * π * r³ ;

=
`(4)/(3)` * π * (7 mm)³ ;

=
`(4)/(3)` * π * (7 * 7 * 7 * mm³) ;

=
`(4)/(3)` * π * (49 * 7 * mm³) ;

=
`(4)/(3)` * π * (343 mm³) ;

=
`(4* 343 mm^3)/(3)`) * π mm³

= (
`(1372 mm^3)/(3)`) * π mm³ ;

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2) Using "3.14" for "π" :
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V =
`(4)/(3)` * π * r³ ;

=
`(4)/(3)` * (3.14)* (7 mm)³ ;

=
`(4)/(3)` * (3.14) * (7 * 7 * 7 * mm³) ;

=
`(4)/(3)` * (3.14) * (49 * 7 * mm³) ;

=
`(4)/(3)` * (3.14) * (49 * 7 * mm³) ;

=
`(4)/(3)` * (3.14) * (343 mm³) ;

= {
`(4)/(3)` } * (3.14 * 343 mm³) ;

= {
`(4)/(3)` } * (1077.02 mm³) ;

= (4 * 1077.02 mm³) / 3 ;

= (4308.08 mm³) / 3 ;
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= 1436.0266666666666667 mm³ ; round to: " 1436.027 mm³ " ;

or; write as: " 1436
`(2)/(75)` mm³ " .
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