A solid metal cube with an edge length of 9 inches is melted down and reshaped into a sphere. Which of the following is the surface area of the sphere to the nearest tenth of an inch?
a)90.5 square inches
b)254.5 square inches
c)391.7 square inches
d)574.8 square inches

Question

A solid metal cube with an edge length of 9 inches is melted down and reshaped into a sphere. Which of the following is the surface area of the sphere to the nearest tenth of an inch?
a)90.5 square inches 
b)254.5 square inches 
c)391.7 square inches 
d)574.8 square inches

dengeki_daisy · Answer

can you help me

bmk614 · Answer

Find the area of the cube using the formula 6x^2.

mrnood · Answer

no - that will not help

find the VOLUME of the cube

bmk614 · Answer

Sorry that is what I meant, that is to formula for the volume.

dengeki_daisy · Answer

Oh okay

mrnood · Answer

the sphere will  have the same volume

the volume a f a sphere is
V = 4 pi r^3/3

so you know the volume  - you can work out radius of the sphere

bmk614 · Answer

What do you get as the volume?

mrnood · Answer

that is not the formula for volume

bmk614 · Answer

@MrNood I am trying to walk through the steps... I am not talking to you. I know it is not the formula for the volume.

mrnood · Answer

@dengeki_daisy 
the cube has a side of 9 in

first step is to find the VOLUME of the cube

I assume you know how to work out the volume from the side

dengeki_daisy · Answer

Okay I'll find it, yes I know how to work it. I'll go ahead and work it out.  (:

mrnood · Answer

The sphere will  have the same volume

the volume of a sphere is
V = 4 pi r^3/3

so you know the volume   - you can work out radius of the sphere

mrnood · Answer

Once you know th eradius

the area of a sphere is
A = 4 pi r^2  

you know r  so you can work out A

dengeki_daisy · Answer

So, just to be sure, would my volume be 729?

mrnood · Answer

yes

dengeki_daisy · Answer

is the answer c

dengeki_daisy · Answer

bmk614

dengeki_daisy · Answer

@bmk614

dengeki_daisy · Answer

??

welshfella · Answer

the volume of the sphere is  ( 4 pi r^3)/ 3

and this is 729 cm^3

so we have ( 4 pi r^3)/ 3 = 729

solve this for  r which is the radius of the sphere

then plug this value of r into the formula for surface area of the sphere wihch is 4 pi r^2

dengeki_daisy · Answer

Okay but how will I find the radius

mrnood · Answer

729 = 4*pi * r^3/3

so

multiply both sides by 3
divide both sides by 4 pi

that gives you r^3

take the cube root to find r


you can then use that value of r to find the area using

A = 4 pi r^2