a cylinder has a radius of 3cm and a length of 10cm every dimention of the cylinder is multiplied by 3 to form a new cylinder how is the ratio of the volumes related the ratio of corresponding dimensions? how would i do this?

Volume of cylinder = area of the base * height , or

V = pi*(r^2)*h
V,original = pi*(3^2)(10)
*you solve for this.

then for the new one,
r,new = 3*3 = 9
h,new = 3*10 = 30
V, new = pi*(9^2)(30)
you solve also for this.

then compare their volumes, find:
(V,new)/V

so there,, hope this helps~ :)

Thank you

is the answer 27?

yes,, (V,new)/V = 27,,

and ration of dimensions is 3 (because it is tripled according to problem)

now, how is 27 related to 3?

Y=5x;(15, -3)

How is the ratio of the volumes related to the ratio of corresponding dimensions?

To find the ratio of the volumes of the original cylinder to the new cylinder, you need to understand that the volume of a cylinder is directly proportional to the square of its radius and its height (length).

In this problem, the dimensions of the original cylinder are multiplied by 3 to form the new cylinder. The new radius would be 3 times the original radius (3 cm x 3 = 9 cm), and the new length would be 3 times the original length (10 cm x 3 = 30 cm).

Now let's calculate the ratio of the volumes using the formula for the volume of a cylinder:

Volume of the original cylinder = π * (radius^2) * height
Volume of the new cylinder = π * (new radius^2) * new height

Substituting the values:
Volume of the original cylinder = π * (3 cm)^2 * 10 cm
Volume of the new cylinder = π * (9 cm)^2 * 30 cm

Simplifying:
Volume of the original cylinder = π * 9 cm^2 * 10 cm
Volume of the new cylinder = π * 81 cm^2 * 30 cm

Now, calculate the ratio:
Ratio of the volumes = (Volume of the new cylinder) / (Volume of the original cylinder)
= (π * 81 cm^2 * 30 cm) / (π * 9 cm^2 * 10 cm)
= (81 cm^2 * 30 cm) / (9 cm^2 * 10 cm)

Canceling out units and simplifying:
Ratio of the volumes = (9 * 9 * 10) / (9 * 10)
= 9

Therefore, the ratio of the volumes of the new cylinder to the original cylinder is 9:1.