Answer:
<u>The diameter of the smaller can is ≅ 9.14 cm</u>
Correct statement and question:
Two cylindrical cans are mathematically similar.
The larger can has a capacity of 1 liter and a diameter of 12 cm and the smaller can has a capacity of 440 ml.
Calculate the diameter, d, of the 440 ml can.
Source:
Previous question that can be found at brainly
Step-by-step explanation:
Let's recall that:
A. The formula of the volume of a cylinder is π*r²*h, where:
r is the radius of the cylinder (half of the length of the diameter) and h, represents the height of the cylinder.
B. 1 liter = 1,000 milliliters = 1,000 cubic centimeters
Therefore, we can find the height of the larger can, this way:
V = π*r²*h
Replacing with the value we know:
d = 12 ⇒ r = 6
1,000 = 3.1416 * 6² * h
1,000 = 113.0976h
h = 1,000/113.0976
h = 8.84 cm (rounding to the next hundredth)
Now we can find the ratio of the radius to the height of the larger can to find the measures of the smaller can, this way because the cylinders are mathematically similar:
Ratio = Radius/Height
Ratio = 6/8.84
Ratio = 0.6787
It means the radius of the smaller can is 0.6787 multiplied by the value of the height of the smaller can. Let x represent the height h of the smaller can, we can write this equation to solve for x:
V = π*r²*h
Replacing with the values we know:
height = x
radius = 0.6787x
440 = π * (0.6787x)² * x
440 = 3.1416 * 0.4606x² * x
440 = 1.4471x³
x³ = 440/1.4471
x³ = 304.06
∛x = ∛304.06
x = 6.73 ⇒ height of the smaller can = 6.73 cm and radius of the smaller can = 6.73 * 0.6787 = 4.57
If radius = 4.57 cm ⇒ diameter = 2 * 4.57 = 9.14 cm
<u>The diameter of the smaller can is ≅ 9.14 cm</u>
