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Write an expression in factored form to represent the volume in the canister not occupied by the tennis balls.
Assume the canister is cylinder with volume V = π r2 h.

Write An Expression In Factored Form To Represent The Volume In The Canister Not Occupied By The Tennis Balls Assume The Canister Is Cylinder With Volume V Π R2 class=

Sagot :

semsee45

Answer:

[tex]\implies V=\pi r^2(h-4 r)[/tex]

Step-by-step explanation:

Volume of the canister LESS the volume of 3 tennis balls:

[tex]V=\pi r^2h-3\left(\dfrac43\pi r^3\right)[/tex]

Expand brackets:

[tex]\implies V=\pi r^2h-4\pi r^3[/tex]

Factor:

[tex]\implies V=\pi r^2(h-4 r)[/tex]

Canister is a cylinder

[tex]\\ \rm\rightarrowtail V=\pi r^2h-3(\dfrac{4}{3}\pi r^3)[/tex]

[tex]\\ \rm\rightarrowtail V=\pi r^2h-\dfrac{12}{3}\pi r^3[/tex]

[tex]\\ \rm\rightarrowtail V=\pi r^2h-4\pi r^3[/tex]

  • Take πr^2 common

[tex]\\ \rm\rightarrowtail V=\pi r^2(h-4r)[/tex]

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