The radius and the height of the cylinder are multiplied by 1/3. What will be the effect on the volume of the cylinder?

Let's start with the base equation:

V = πr²h

If we multiply the radius and height by 1/3, we get:

V₁ = π(r/3)²(h/3)

Now simplify:

V₁ = π(r²/9)(h/3)
V₁ = πr²h/27

Since we know that:

V = πr²h

substitute in "V" in place of "πr²h" to get:

V₁ = V/27

So now you can see that the volume will be multiplied by 1/27.

(1/3)^2 because of radius
1/3 because of height, so
(1/3)^2 * (1/3) = 1/27

V = pi * r^2 * h

r → r/3 , h → h/3

The new V : pi * (r/3)^2 * (h/3)
= pi * r^2/9 * h/3
= (1/27) pi * r^2 * h

The volume is multiplied by 1/27.