Aspherical balloon has a 32-in. diameter when it is fully inflated. half of the air is let out of the balloon. assume that the balloon remains a sphere.

a. find the volume of the fully-inflated balloon.
b. find the volume of the half-inflated balloon.
c. what is the radius of the half-inflated balloon?

Volume of Fully-inflated balloon: 17148.58 inches^3

Volume of half-inflated balloon: 8574.29 inches^3

Radius of half-inflated balloon: 12.7 inches

Step-by-step explanation:

Given

Diameter of inflated balloon=d=32 inches

As we have to use the radius of the balloon to calculate the volume then,

r=d/2

r=32/2

r=16 inches

Then balloon can be sphere when it has gas in it.  

Volume of fully-inflated balloon:

Vhf=4/3 πr^3

=4/3*3.14*(16)^3

=12.56/3*4096

=51445.76/3

=17148.58 inches^3

Volume of Half-Inflated balloon:

As there will be half of the gas left, so the volume of half-inflated balloon will be the half of fully-inflated balloons volume.

Vh=Vf/2

=17148.58/2

=8574.29 inches^3

Radius of Half-inflated balloon:

As we know the volume of half inflated balloon, we will use the formula for volume to calculate the radius.

Vh=4/3 πr^3

8574.29=4/3*3.14*r^3

8574.29*3/4*1/3.14=r^3

r^3=2047.999

∛r= ∛2047.999

So,

r=12.69 ≈12.7 inches

d

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!

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:

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.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: