Geometry Problem, I doubt anybody will do it, but..I don't know.?

Question

When making a snowman out of three snow spheres, let’s have the ratio of the diameter of each of the three spheres be 1:2:3. If the diameter of the smallest sphere (the top) is 18 inches, what is the diameter, in feet, of the largest sphere (the bottom) of the snowman? Express your answer as a decimal to the nearest tenth.
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What is volume of the middle sphere, in cubic inches? Express your answer in terms of pi. The formula for the volume of a sphere is (4/3)(pi)r3.
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What is the ratio of the volume of the smallest sphere to the volume of the middle sphere? Express your answer in the form a:b.
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Assuming that our three spheres are placed one on top of the other with no "smushing" or "denting" of the spheres, how many feet tall is our snowman?



Can you help me out, or you don't have to tell me the answer, just can you tell me what steps I need to do to find the answer?

Answer 1

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.

Answer 2

For the first one, just use the ratio. The middle sphere is twice as thick as the top one, and the bottom is three times as thick. So the bottom's diameter is 18*3 or 54 inches, which is 4.5 feet.

For the second one, remember that the radius is half of the diameter and the middle sphere's diameter is twice the top sphere's diameter. So the radius of the middle sphere is the same as the diameter of the top sphere: 18 inches. Cube that and you get 5832 in^3. Multiply by 4/3 pi and you get 7776pi in^3.

The third one could be done by finding the volumes of both spheres, but there's an easier way. Remember, the ratio of the diameters of the top and middle spheres is 1:2. The volume is related to the diameter cubed, so when the diameter increases by a factor of 2, the volume increases by a factor of 8 (2^3). Therefore, the ratio of the volumes is 1:8.

As for the last one, if you stack three perfect spheres on top of one another without squashing them, the height is simply the sum of their diameters. The top sphere's is 18, the middle's is twice 18 or 36, and the bottom's is 3*18 or 54. Add them all together to get 108 inches, or 9 feet.

Answer 3

If each and each and every interior perspective measures one hundred sixty 5°, then each and each and every outside perspective measures 15°. because the sum of the exterior angles is 360°, then the variety of aspects is 360°/15° = 24. There are 24 aspects.

Answer 4

the answer to the first one is 4.5

18 inches = 1
36 inches = 2
54 inches = 3

54/12 = 4.5"

Answer 5

1. 54"
2. 432pi
3. 1:2
4. 108" or 9 ft.

Answer 6

~Edit~ I didn't read all of the instructions, and put everything in "feet" instead of inches. Puzzling has my vote for best answer, he explained it very well.

Answer 7

What is the purpose of this calculation?

Answer 8

no