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The volume of a cylinder varies jointly with the square of its radius and with its height: v=kr^2h

Cylinder A has a volume of 254.34 cubic inches and has a radius of 3 inches and a height of 9 inches. What is the volume of cylinder B, which has a radius of 4 inches and a height of 5 inches?

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Given:  v=kr^2h 


Here you have 2 choices:  you could "cheat" by recalling that the formula for the volume of a cyl. is Vc = pi*r^2(h), and thus recognize that k = pi.  
  
or you could plug in the given info to find the const. of proportionality, k.


Using  Vc = pi*r^2*h, for r = 4 in and h = 5 in, 

Cyl. B has volume  pi*(4 in)^2*(5 in) = 251.33 cu in  (ans)

Answer:

Volume of the cylinder B is 251.2 inches³ .

Step-by-step explanation:

As given

The volume of a cylinder varies jointly with the square of its radius and with its height .

V = kr²h

As given

Cylinder A has a volume of 254.34 cubic inches and has a radius of 3 inches and a height of 9 inches.

V = 254.34 cubic inches

r = 3 inches

h = 9 inches

Put all the values in the above formula

254.34 = k × 3 × 3 × 9

254.34 = 81k

[tex]k=\frac{254.34}{81}[/tex]

k = 3.14

As given

Cylinder B, which has a radius of 4 inches and a height of 5 inches .

r = 4 inches

h = 5 inches

k = 3.14

Put all the values in the formula

V = 3.14 × 4 × 4 × 5

V = 251.2 inches³

Therefore the volume of the cylinder B is 251.2 inches³ .

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