Question

The radius of the base of the cylinder is 2x cm and the height of the cylinder is h cm.

Answer 1

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 = $\frac{1}{3}$$\pi$$r^{2}$h

where: r is its base radius and h the height

volume of the given cylinder = $\frac{1}{3}$$\pi$ x $(2x)^{2}$ x h

                                              = $\frac{1}{3}$$\pi$ x 4$x^{2}$ x h

                                              = $\frac{4}{3}$$\pi$$x^{2}$ h

volume of a sphere = $\frac{4}{3}$$\pi$$r^{3}$

where r is the radius.

volume of the given sphere =  $\frac{4}{3}$$\pi$ x $(3x)^{3}$

                                         =  $\frac{4}{3}$$\pi$ x 9 $x^{3}$

                                         = 12$\pi$$x^{3}$

Since,

volume of the cylinder = volume of the sphere

Then we have;

$\frac{4}{3}$$\pi$$x^{2}$ h = 12$\pi$$x^{3}$

4$\pi$$x^{2}$ h = 36$\pi$$x^{3}$

subtract $x^{2}$ from both sides

4$\pi$h = 36$\pi$x

divide both sides by 4$\pi$

h = $\frac{36\pi x}{4\pi }$

  = 9x

h = 9x