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.
packing foam needed =

volume of packing foam to fill the rest of the box = 1279.31 inches³

Step-by-step explanation:

The basket ball is a sphere

volume of the ball = 4/3πr³

r = 9.5/2 = 4.75 inches

volume of the ball = 4/3πr³

volume of the ball = 4/3 × 3.14 × 4.75³

volume of the ball = 4/3 × 3.14 × 107.171875

volume of the ball = 1346.0787500/3

volume of the ball = 448.69291667 inches³

The volume of the box

volume of box = L³

where

L = 12 inches

volume of box = L³

volume of box = 12³

volume of box = 1728 inches³

volume of box = L³

The volume of empty space to fill the foam is the difference of the volumes.

= 1728 inches³ - 448.69291667 inches³

volume of packing foam to fill the rest of the box = 1279.31 inches³

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

do have an equation or graph or

step-by-step explanation: