A gas tank has ends that are hemispheres of radius r ft. the cylindrical midsection is 6 ft long. express the volume of the tank as a function of r?

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A gas tank has ends that are hemispheres of radius r ft. the cylindrical midsection is 6 ft long. express the volume of the tank as a function of r?

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Answer 1 · 2015-10-15T10:04:34

$v_("all") (ft^3)= (6pir^2 + 4/3 pi r^3) ft^3$

Explanation:

Let volume be v then:
Given: radius is r
Let length of cylinder be L

Volume of two ends when put together form a sphere
$v_("sphere") = 4/3 pi r^3$ ........ ( 1 )

Volume of cylinder is circle area times length of cylinder
$v_("cylinder")= pi r^2 L$
But $L$ = 6 (feet) giving
$v_("cylinder")= 6pi r^2$ ........ ( 2 )

Both r and L are both measured in feet. so you can add the volumes directly, giving:

Putting the two together: ( 1 ) + ( 2 )

$v_("all")= 6pir^2 + 4/3 pi r^3$

Let feet be ft
$v_("all") (ft^3)= (6pir^2 + 4/3 pi r^3) ft^3$

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A gas tank has ends that are hemispheres of radius r ft. the cylindrical midsection is 6 ft long. express the volume of the tank as a function of r?

1 Answer

Explanation:

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