Question

What is the ratio of the volumes of two similar rectangles, if the ratio of their perimeters is 2:9? ​

Answer 1

Answer:

Step-the base is equal to length * width.

the formula for the volume of a rectangular prism becomes length * width * height.

the ratio of the volume of a three sided figure is the ratio of their corresponding sides cubed.

so if the ratio of their volumes is 125/64, then the ratio of their corresponding sides id 5/4 because 5^3 = 125 and 4^3 = 64.

since the base area is equal to length * widfth, then the ratio of the areas becomes 5^2 / 4^2 which is equal to 25/16.

the ratio of the base area becomes 25/16.

to confirm, use an example:

original prism has dimensions as shown below:

length = 20

width = 40

height = 60

volume = 20 * 40 * 60 = 48000

base area = 20 * 40 = 800

prims that has sides in a ratio of 5/4 to original prism is shown below:

length = 20 * 5/4 = 25

width = 40 * 5/4 = 50

height = 60 * 5/4 = 75

volume = 25 * 50 * 75 = 93750

base area = 25 * 50 = 1250

ratio of the volumes = 93750 / 48000 = 1.953125

ratio of the base areas = 1250 / 800 = 1.5625

125/64 = 1.953125

25/16 = 1.5625

the formulas work.

the ratio of the volume is 125/64

the ratio of the base area is 25/16by-step explanation:

volume = 20 * 40 * 60 = 48000

base area = 20 * 40 = 800

prims that has sides in a ratio of 5/4 to original prism is shown below:

length = 20 * 5/4 = 25

width = 40 * 5/4 = 50

height = 60 * 5/4 = 75

volume = 25 * 50 * 75 = 93750

base area = 25 * 50 = 1250