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podryga [215]
1 year ago
6

Propane is stored in a cylindrical tank with a diameter of 15 inches and a height of 48 inches. Which equation could be used to

determine the radius of a spherical tank with the same volume?
Mathematics
1 answer:
Virty [35]1 year ago
8 0

Step-by-step explanation:

remember. the radius is always half the diameter.

volume of a cylinder

pi × r² × height

pi×7.5²×48 = pi×56.25×48 = 8,482.300165... in³

volume of a sphere

4/3 × pi × r³

and that volume should be the same as the cylinder. so,

4/3 × pi × r³ = pi×56.25×48

4/3 × r³ = 56.25 × 48

1/3 × r³ = 56.25 × 12

r³ = 56.25 × 36 = 7.5² × 6² = (7.5×6)² = 45² = 2025

r =  \sqrt[3]{2025}

which would be 12.65148998... in.

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This is a problem of maxima and minima using derivative.

In the figure shown below we have the representation of this problem, so we know that the base of this bin is square. We also know that there are four square rectangles sides. This bin is a cube, therefore the volume is:

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That is:

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We also know that the <span>bin is constructed from 48 square feet of sheet metal, s</span>o:

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Therefore, the total area of the cube is:

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V =  x^{2}( \frac{48- x^{2} }{x}) = 48x- x^{3}

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</span>
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And its volume is:

V = (4^{2} )(2) = 32 ft^{3}

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