Answer:
The sphere is taller than the cube
Step-by-step explanation:
we know that
The height of the cube is equal to the length side of the cube and the height of the sphere is equal to the diameter of the sphere
step 1
Find the length side of the cube
we know that
The volume of the cube is equal to
[tex]V=b^{3}[/tex]
where
b is the length side of the cube
we have
[tex]V=10\ in^{3}[/tex]
substitute and solve for b
[tex]10=b^{3}[/tex]
[tex]b=\sqrt[3]{10}\ in[/tex]
[tex]b=2.15\ in[/tex]
step 2
Find the diameter of the sphere
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]V=10\ in^{3}[/tex]
substitute and solve for r
[tex]10=\frac{4}{3}\pi r^{3}[/tex]
[tex]\frac{30}{4}=\pi r^{3}[/tex]
[tex]r=\sqrt[3]{\frac{30}{4\pi}}[/tex]
[tex]r=1.34\ in[/tex]
Find the diameter
[tex]D=2r=2*1.34=2.68\ in[/tex]
step 3
Compare
[tex]2.68\ in > 2.15\ in[/tex]
therefore
The sphere is taller than the cube
