Answer:
see the explanation
Step-by-step explanation:
we know that
The volume of a cone is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
[tex]V=48\pi\ units^3[/tex]
so
[tex]48\pi=\frac{1}{3}\pi r^{2}h[/tex]
Simplify
[tex]144=r^{2}h[/tex] ----> equation A
step 1
Cone a
[tex]r_a=6\ units\\h_a=4\ units[/tex]
Verify
substitute the given values in equation A
[tex]144=r^{2}h[/tex]
[tex]144=6^{2}(4)[/tex]
[tex]144=144[/tex] ---> is true
step 2
Cone b
Assume the value of the radius and with the equation A calculate the value of the height
so
For [tex]r=5\ units[/tex]
substitute in the equation A
[tex]144=r^{2}h[/tex]
[tex]144=5^{2}h[/tex]
solve for h
[tex]144=25h[/tex]
[tex]h=5.76\ units[/tex]
Verify
substitute the given values in equation A
[tex]144=r^{2}h[/tex]
[tex]144=5^{2}(5.76)[/tex]
[tex]144=144[/tex] ---> is true
The value of r and h satisfy the equation A, that means the volume of cone b is the same that volume of cone a
