Question

The ratio of the base^9:16 areas of two similar copper cylinders is:

(a) Find the rate of the base of the cylinders.
(b) Find the ratio of the volumes of the cylinders.
(c) If the height of the smaller cylinder is 5kg, find the mass of the largest cylinder.

Answer 1

The rate of the base of the cylinders is 3:4. The ratio of the volumes is 9:16. The mass of the largest cylinder depends on the density of copper.

Step-by-step explanation:

To find the rate of the base of the cylinders, we can set up a ratio using the formula for the area of a circle, A = πr2. Let's call the base of the smaller cylinder r1 and the base of the larger cylinder r2. So the ratio of their areas is:

(r12) / (r22) = 9:16

To find the rate of the base, we take the square root of both sides:

r1 / r2 = 3/4

So the rate of the base of the cylinders is 3:4.

To find the ratio of the volumes, we use the formula for the volume of a cylinder, V = πr2h. The ratio of the volumes is:

(r12h1) / (r22h2) = 9:16

Finally, if the height of the smaller cylinder is 5 units, we can use the volume ratio equation to find the height of the larger cylinder:

(r12h1) / (r22h2) = 9/16

Substituting the known values, we get:

(r12) / (r22) * (h1 / h2) = 9/16

Plugging in r1 = 3, h1 = 5, and solving for r2 gives:

r2 = 4, h2 = 20

Therefore, the mass of the largest cylinder would depend on the density of copper.