Question

*PLEASE HELP, DIFFICULT QUESTION* What is the total volume of snow used to make the snowman if the head is 12 inches wide, the middle is 16 inches wide, and the bottom is 18 inches wide? (Use 3.14 for pie)

Answer 1

The correct answer is:

6,099.97 cubic inches.

To calculate the total volume of snow used to make the snowman, we need to treat each part of the snowman as a sphere and calculate the volume of each sphere. The volume of a sphere is given by the formula:

`\[ V = (4)/(3) \pi r^3 \]`

where V is the volume,
`\( \pi \)` is Pi (approximately 3.14 as given in the question), and r is the radius of the sphere.

The diameters of the snowman's parts are given, so we will divide them by two to get the radii:

- Head radius:
`\( (12)/(2) = 6 \) inches`

- Middle radius:
`\( (16)/(2) = 8 \) inches`

- Bottom radius:
`\( (18)/(2) = 9 \) inches`

Now we'll calculate the volume for each part:

1.
`Head volume: \( V_(head) = (4)/(3) \pi (6)^3 \)`

2.
`Middle volume: \( V_(middle) = (4)/(3) \pi (8)^3 \)`

3.
`Bottom volume: \( V_(bottom) = (4)/(3) \pi (9)^3 \)`

Then, we'll sum these volumes to get the total volume of snow used to make the snowman:

`\[ V_(total) = V_(head) + V_(middle) + V_(bottom) \]`

Let's calculate the total volume.

The total volume of snow used to make the snowman, with each part of the snowman treated as a sphere, is approximately 6,099.97 cubic inches.

Answer 2

6103.07 inches ^ 3

Explanation:

Step 1: Find the volume of the head

d = 12

r = d/2

r = 6

`=(4)/(3) (3.14)6^(3) \\=904.78 inches^(3)`

Step 2: Find the volume of the body

d = 16

r = d/2

r = 8

`=(4)/(3) (3.14)8^(3) \\=2144.66inches^(3)`

Step 3: Find the volume of the legs

d = 18

r = d/2

r = 9

`=(4)/(3) (3.14)9^(3) \\=3053.63 inches^(3)`

Step 4: Add the volumes together

`904.78 +2144.66+3053.63=Volume`

`6103.07=Volume`

Therefore the volume of the snowman is 6103.07 inches ^ 3