A cylinder is 8cm high and its base diameter is 4cm.The height of a similar cylinder is 12cm. The height of a similar cylinder is 12cm.find the diamter of the base of the larger cylinder

clearly the scale is 1:3

So, multiply the diameter by 3.

To find the diameter of the base of the larger cylinder, we can set up a proportion based on the similarity of the two cylinders.

First, let's define the variables:
- Let D1 be the diameter of the base of the smaller cylinder.
- Let D2 be the diameter of the base of the larger cylinder.
- Let H1 be the height of the smaller cylinder.
- Let H2 be the height of the larger cylinder.

Based on the given information, we have:
D1 = 4 cm (diameter of the smaller cylinder)
H1 = 8 cm (height of the smaller cylinder)
H2 = 12 cm (height of the larger cylinder)

We can set up the proportion:

(D1 / H1) = (D2 / H2)

Plugging in the values we know, we get:

(4 cm / 8 cm) = (D2 / 12 cm)

Simplifying the left side, we have:

1/2 = D2 / 12 cm

Now, we can solve for D2 by multiplying both sides by 12 cm:

1/2 * 12 cm = D2

6 cm = D2

Therefore, the diameter of the base of the larger cylinder is 6 cm.