Question

A basketball with a diameter of 9.5 in. is placed in a cubic box with sides 12 in. long. How many cubic inches of packing foam are needed to fill the rest of the box? Round to the nearest tenth.

Answer 1

1279.3 cubic inches (Rounded to the nearest tenth)

Explanation:

Side of a cubic box = 12 inches

volume of cubic box =
`side^3` (since side is equal to 12 inches)

=
`12^3` = 1,728 cubic inches

It means that box can be filled with 1,728 cubic inches of any material

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But, it is given that it has one basketball placed in it.

hence we need to find the volume of basketball .

Since basket ball is spherical in shape

formula to calculate its volume will be same as that of formula to calculate volume of sphere

volume of sphere =
`(4/3 ) \pi r^3\\` where r is the radius of sphere

radius of basketball = diameter/2 = 9.5/2 in = 4.75 inches

therefore volume of basket ball is given by

volume of basketball =
`(4/3 ) \pi r^3\\\\\\=>(4/3 ) \3.14* 4.75^3\\\\\\= 448.693 \ cubic \ inches`

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In box with volume 1,728 cubic inches,, 448.693 cubic inches is occupied by basketball.

It means rest is empty which can be filled with foam.

To calculate the empty space, we subtract volume of basket ball from volume of box

volume of empty space = volume of box - volume of basket

= 1728 - 448.693 = 1279.307 cubic inches

1279.307 cubic inches in nearest tenth will be 1279.3 cubic inches.

Hence, 1279.3 cubic inches of foam are needed to fill the rest of the box