Mathematics, 10.12.2019 09:31 carminamtzb3725

You have just opened a small business selling sports equipment . you are packaging basketballs inside boxes that are cubes . the volume of the box is 729 cubic feet . the basketball fits perfectly in the box without additional room at the point of the circumference of the ball . what is the volume of the basketball ? what is the volume of the space not occupied by the ball ?

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Answer from: deborah0

Part A) The volume of the basketball is $V=121.5\pi\ ft^3$

Part B) The volume of the space not occupied by the ball is $V=(729-121.5\pi)\ ft^3$

Step-by-step explanation:

step 1

Find the length side of the cube (box)

we know that

The volume of a cube is equal to

V=b^3

where

b is the length side of the cube

we have

$V=729\ ft^3$

b^3=729

$b=\sqrt[3]{729}\ ft$

$b=9\ ft$

step 2

Find the volume of the basketball

we know that

The volume of a sphere (basketball) is equal to

$V=\frac{4}{3}\pi r^{3}$

we have that

The diameter of the basketball is equal to the length side of the cube

$r=9/2=4.5\ ft$

substitute

$V=\frac{4}{3}\pi (4.5)^{3}$

$V=121.5\pi\ ft^3$

step 3

Find the volume of the space not occupied by the ball

we know that

The volume of the space not occupied by the ball is equal to the volume of the box minus the volume of the ball

$V=(729-121.5\pi)\ ft^3$

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

Answer from: Quest

step-by-step explanation:

a difference is the result of subtraction. while each of these expressions has subtraction in it, a difference will be the result when subtraction is the last operation applied in the order of operations for the expression. this means subtraction must be outside of the parenthesis. only b has this.

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