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

answer: -1

step-by-step explanation:

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."