Manuel bought a balloon (that is a perfect sphere) with a radius of 2 cm. he wanted his balloon to be bigger, so he blew 2 big breaths of air into the balloon. each big breath increased the balloon's radius by 1 cm.

I guess we want to evaluate how much the volume of the balloon changes in each blow.

The volume of a sphere can be written as:

v = (4/3)*pi*r^3

where pi = 3.1416 and r is the radius of the sphere.

we have that initially, the radius of the sphere is r = 2cm

then v0 = (4/3)*3.1416*(2cm)^3 = 33.5 cm^3

now, after one blow, the radius is 3 cm, so we have:

v1 = (4/3)*3.1416*(3cm)^3 = 113.1cm^3

this means that the change in volume is  

v1 - v0 = 97.6cm^3

and after the other blow, we have that the radius is 4cm:

v2 = (4/3)*3.1416*(4cm)^3 = 268.1cm^3

the change in the volume is:

v2 - v1 = 154.9 cm^3

So we can see that the change of 1cm in the radius has a bigger impact if the initial radius of the sphere is bigger.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .