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6. A box in the shape of a cube has an interior side length
of 18 inches and is used to ship a right circular
cylinder with a radius of 6 inches and a height of
12 inches. The interior of the box not occupied by the
cylinder is filled with packing material. Which of the
following numerical expressions gives the number of
cubic inches of the box filled with packing material?
F. 6(18)2 – 21(6)(12) – 29(
62
G. 6(18)2 – 27(6)(12)
H. 183 - T(6)(12)
J. 183 - T(6)(12)
K. 183 - T(12)
ob ..

Respuesta :

Answer:

think it is 183 - π(6)2(12) or J because it is the closes

Volume of packing materials = Volume of box - volume of cylinder

Since the box has same shape as a cube, the volume = L3

Where L is the lenght of the box

Volume of a right circular cylinder = πr2h

where r is the radius and h is the height

Volume of packing materials = L3 - πr2h

hope this will or can (even maybe) helps

The number of cubic inches of the box which is filled with packing material is 5194.83 cubic inches approx.

How to find the volume of the substance in an object?

Volume is the measure of the 3 dimensional space occupied by the object.

If the filled substance occupies almost the whole inside of the considered object, then the volume of the material in the object is the space it occupies, which is equal to the space inside that box, which is its interior volume.

What is the volume of a right circular cylinder?

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

For the given case, the packing material occupies whatever space is left in the box, after that cylinder is putted inside of the box.

Volume of the packing material filled in the box = Volume of the remaining space of the box after cylinder is placed = Volume of box - Volume of the cylinder in the box

Now, volume of the box = cube of its side length (as box is cubic, so we used formula for volume of a cube which is its side cubed),

Volume of the box = [tex]18^3 = 6552[/tex] cubic inches

Volume of cylinder =

[tex]V = \pi r^2 h \: \rm unit^3 = \pi \times (6)^2 \times 12 = 432\pi\\ V \approx 1357.17 \: \rm inch^3[/tex]

Thus, volume of the remaining space = [tex]6552 - 1357.17 = 5194.83 \: \rm inch^3[/tex]

This is the amount of space left in the box, the same amount of space the packing material will occupy.

Thus, the number of cubic inches of the box which is filled with packing material is 5194.83 cubic inches approx.

Learn more about volume of cylinder here:

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