Answer:
h = 9x
Step-by-step explanation:
Given: i. for the cylinder, base radius = 2x cm, height = h cm
ii. for the sphere, radius = 3x cm
iii. volume of the cylinder = volume of the sphere
volume of a cylinder is given as;
volume = [tex]\frac{1}{3}[/tex][tex]\pi[/tex][tex]r^{2}[/tex]h
where: r is its base radius and h the height
volume of the given cylinder = [tex]\frac{1}{3}[/tex][tex]\pi[/tex] x [tex](2x)^{2}[/tex] x h
= [tex]\frac{1}{3}[/tex][tex]\pi[/tex] x 4[tex]x^{2}[/tex] x h
= [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]x^{2}[/tex] h
volume of a sphere = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
where r is the radius.
volume of the given sphere = [tex]\frac{4}{3}[/tex][tex]\pi[/tex] x [tex](3x)^{3}[/tex]
= [tex]\frac{4}{3}[/tex][tex]\pi[/tex] x 9 [tex]x^{3}[/tex]
= 12[tex]\pi[/tex][tex]x^{3}[/tex]
Since,
volume of the cylinder = volume of the sphere
Then we have;
[tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]x^{2}[/tex] h = 12[tex]\pi[/tex][tex]x^{3}[/tex]
4[tex]\pi[/tex][tex]x^{2}[/tex] h = 36[tex]\pi[/tex][tex]x^{3}[/tex]
subtract [tex]x^{2}[/tex] from both sides
4[tex]\pi[/tex]h = 36[tex]\pi[/tex]x
divide both sides by 4[tex]\pi[/tex]
h = [tex]\frac{36\pi x}{4\pi }[/tex]
= 9x
h = 9x
