Question

Two spherical pieces of cookie dough have radii of 3cm & 5cm. The pieces are combined to form one large spherical piece of dough. What is the approximate radius of the new sphere of dough?
Round to the nearest tenth.

Answer 1

@jim_thompson5910 where do i start

Answer 2

Start by finding the volume of the two original spheres:
V=4/3pi*r^3

Answer 3

ok!

Answer 4

i got v=113.04 and v=523.3

Answer 5

yes! So now you have to realize that the total volume doesnt change just because you combine the two spheres. So whats your total volume?

Answer 6

total volume is 636.34

Answer 7

Right, so the total volume before has to be the same as the total volume after since you arent adding or subtracting any dough.

Therefore you know the volume of the final sphere is 636.34 cm^3

All you have to do now is remember that V=4/3pi*r^3

You know volume, and you want to solve for radius, so now you just have to solve for radius.

by rearranging the equation you get that
r^3=V/(4/3pi)
and r = [V/(4/3pi)]^(1/3)

now just plug in V :)

Answer 8

r= 2664.14346667^(1/3)
how do i do the rest @LifeEngineer

Answer 9

do you have a calculator?

I can't imagine that anyone would have you do such an awful cubic root without one

Taking the cubic root of a number, and raising it to the third power
\[\sqrt[3]{x} = x ^{1/3}\]
are the same thing mathematically. Most calculators only have a square root, but will have a power function (usually something looking like
"^" or \[x^y\]
Anyways just taking the cubic root of 2663.14.... cm^3 is easy enough and gives you
r = 13.86285.... cm

Just remember that you were asked to round to the nearest tenth, and you're all set

Answer 10

so 13.9?

Answer 11

yep!

Answer 12

thank you!

Answer 13

wait it said it was wrong?