Answer:
the volume of the sphere is
[tex]33.51 in^{3}[/tex]
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, sphere and cube.
Given data
Volume of cube v = 64 cubic inches
since we are dealing with a cube the height and the radius of the sphere is same as the sides of the cube,
we know that volume of cube is expressed as
[tex]v= l*b*h[/tex]
[tex]v=l^{3}[/tex]
[tex]64= l^{3}[/tex]
[tex]l= \sqrt[3]{64}[/tex]
[tex]l= 4 in[/tex]
also diameter d=length l
Diameter d= [tex]4in[/tex]
Radius r = [tex]\frac{d}{2}[/tex]= [tex]\frac{4}{2}[/tex]= [tex]{2 in}[/tex]
Height h=[tex]4in[/tex]
we know that the volume of a sphere is given by
[tex]v= \frac{4}{3} \pi r^{3}[/tex]
substituting into the formula we have
[tex]v= \frac{4}{3} \ *3.142*2^{3} \\v=\frac{4*3.142*8}3} \\v= \frac{100.54}{3} \\v= 33.52in^{3}[/tex]
