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he volume of a cylinder varies jointly with the base (area) and the height. The volume is 40inches^3 when the base (area) is 6inches^2 and the height is 20inches. Find the volume of the cylinder (after finding the variation constant) when the base (area) is 8inches^2 and the height is 12inches.

Respuesta :

Answer:

Variation factor k = 1/3

New volume when the base (area) is 8inches^2 and the height is 12inches is 32 in3

Step-by-step explanation:

As we know,  

The volume of cylinder (V) is given by πr²h  

Here  πr² = base area and h is the height of the cylinder

V ∞ πr²h

V = kπr²h  

Substituting the given values, we get  

40 = 6 x 20 x k

40 = 120k and

k   = ⁴⁰/₁₂₀

    = ¹/₃.

Volume when base area = 8in² and h = 12 inch

V = 8 x 12 x ¹/₃

V = 32in³

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