PART 1:

If the ratio of the diameters is 1 : 2 : 3, then that means the diameters are 18 : 36 : 54. You can solve this with similar ratios:

1/18 = 2/x

x = 36

1/18 = 3/y

y = 54

So the respective diameters are 18", 36" and 54". (The radii would be half this or 9", 18", 27").

However, the answer is to be expressed in feet so divide by 12:

54 inches / 12 inches/ft = 4.5 feet.

PART 2:

Volume of the *middle* sphere. The radius is 18" (one half of 36"), so just plug this into the formula:

V = (4/3)(pi)(18)^3

V = 7,776 pi (cubic inches)

PART 3:

The volume of the *small* sphere = (4/3)(pi)(9)^3

The volume of the *middle* sphere = (4/3)(pi)(18)^3

To get the ratio between these two, just divide smallest / biggest

= (4/3)(pi)(9^3) / (4/3)(pi)(18^3)

The 4/3 and pi cancel out

= 9^3 / 18^3

= 729 / 5,832

= 1 : 8

This makes sense because the ratio of lengths is linear (1 : 2 : 3), the ratio of areas is squared (1 : 4 : 9) and the ratio of volumes is cubic (1 : 8 : 27).

PART 4:

We have the 3 diameters (18", 36", 54"). the total height is the sum:

18 + 36 + 54 = 108"

Convert this to feet (divide by 12):

108 inches / 12 inches/ft = 9 feet.

PART 1:

If the ratio of the diameters is 1 : 2 : 3, then that means the diameters are 18 : 36 : 54. You can solve this with similar ratios:

1/18 = 2/x

x = 36

1/18 = 3/y

y = 54

So the respective diameters are 18", 36" and 54". (The radii would be half this or 9", 18", 27").

However, the answer is to be expressed in feet so divide by 12:

54 inches / 12 inches/ft = 4.5 feet.

PART 2:

Volume of the *middle* sphere. The radius is 18" (one half of 36"), so just plug this into the formula:

V = (4/3)(pi)(18)^3

V = 7,776 pi (cubic inches)

PART 3:

The volume of the *small* sphere = (4/3)(pi)(9)^3

The volume of the *middle* sphere = (4/3)(pi)(18)^3

To get the ratio between these two, just divide smallest / biggest

= (4/3)(pi)(9^3) / (4/3)(pi)(18^3)

The 4/3 and pi cancel out

= 9^3 / 18^3

= 729 / 5,832

= 1 : 8

This makes sense because the ratio of lengths is linear (1 : 2 : 3), the ratio of areas is squared (1 : 4 : 9) and the ratio of volumes is cubic (1 : 8 : 27).

PART 4:

We have the 3 diameters (18", 36", 54"). the total height is the sum:

18 + 36 + 54 = 108"

Convert this to feet (divide by 12):

108 inches / 12 inches/ft = 9 feet.