Question

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 18 centimeters cubed.

A sphere with height h and radius r. A cylinder with height h and radius r.

What is the volume of the sphere?
12 centimeters cubed
24 centimeters cubed
36 centimeters cubed
54 centimeters cubed

Answer 1

12 cm^3

Explanation:

Before we do anything, we should set up the proportion.

`(\pi * r^2*h)/((4\pi r^3)/(3)) = (18)/(x)`

Now do the Cancelations of \pi r^2 on the left.

h// (4/3) r = 18/x

but h = 2*r

2r // (4/3) * r = 18/x Cancel the rs on the left

2// (4/3) = 18/x Make 2 = 2/1 so you can handle the fraction

2/1 // (4/3) = 18/x Invert and multiply the denominator

2/1 * 3/4 = 18/x

6/4 = 18x You can reduce the left side

3/2 = 18x Cross multiply

3x = 2*18 Combine the right

3x = 36 Divide by 3

x = 12

So what you have found is the volume of the sphere. 12 cm^3

This is a very interesting question. Keep in mind that physics does this all the time for any of the force formulas (but not all).

I'm a little long winded here, but the first time you see this, you should be given very small steps.