Question

I need an idea! pls help

Find the volume of the largest cube that can be cut from a sphere of diameter 5 inches

Answer 1

not great at geometry but i think you cut it so the long diagonal of the cube is the diameter of the sphere
that is my best advice

Answer 2

I think that your problem is equivalent to find the largest quadrilateral enclosed by a circumference.
What is that quadrilateral?
I think that using the differential calculus we can prove that quadrilateral has to be a square

Answer 3

OH I SEE

check this pls

a = any side

if volume of a cube is V = a^3

diameter of a cube is root of 3 x a

then

5 = root of 3 x a , then I solve for a ?

If I want the volume I shall cube a ?

Answer 4

of course, "largest" means "largest area"

Answer 5

@Michele_Laino thanks , we are not yet in calculus though :(

Answer 6

i think that is correct

Answer 7

but i could be wrong
diagonal is 5 so \(s\sqrt3=5\) making \(s=\frac{5}{\sqrt3}\)

Answer 8

to get the volume, cube that one

Answer 9

@satellite73 thanks much! :)