Question

A cube of side 10 cm is melted down and made into ten identical
spheres. Calculate the surface area of one of the spheres.​

Answer 1

Answer:

Step-by-step explanation:

A cube with sides of 10cm will have a surface area of 600cm^2  ( = 6 sides, each one 10 x 10 cm).

The volume of the cube will be 1,000 cm^3  ( = 10 x 10 x 10).

If you melt it down to form ten identical spheres, each of them will have a volume of:

1,000 cm^3 / 10  =  100 cm^3

And the volume of a sphere is:

Vs = 4/3 pi*r^3

So you can calculate the radius of the spheres:

r^3  =  3Vs / 4pi  =  (300) / (12.5664)  =  23.8732 cm^3

r  =  2.8794 cm

Now, you can use the radius to find the surface area of the spheres:

As  =  4pi*r^2  =  (12.5664)(2.8794)^2  =  104.19 cm^2