Two cylindrical cans are mathematically similar.
The larger can has a capacity of 1 litre and the smaller can has a capacity of 440 ml.
Calculate the diameter, d, of the 440 ml can.

The diameter of the smaller can is ≅ 9.14 cm

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

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

The diameter of the smaller can is ≅ 9.14 cm

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺