How many times smaller is the volume of a cylinder if the diameter is multiplied by a half?

Question

I just need help please!!!

Answer 1

The equation for the volume of a cylinder is:

V = πr²h

Your question asks about the diameter, and since diameter = 2r, we can rewrite the above equation as:

V = π(^d/₂)² h

Or

V = π (d²/4) * h

Now, if the diameter is multiplied by 1/2, the equation would be

V = π [(1/2d)²/4] * h

which becomes

V = π [(1/4*d²)/4] * h

V = π (¹/₁₆ d²) * h

When we compare that to the original equation V = π (d²/4) * h we can see the new equation is 1/4 the size of the original one.

So when the diameter is reduced by 1/2 the volume is reduced by 1/4

Answer 2

The volume of a cylinder is proportional to the square of the radius; therefore, multiplying the radius by 1/2 will multiply the volume by 1/4.

V = πr²h