1. Find and simplify the volume-to-surface-area ratio for each of the three possible ice cube shapes. You can use this chart.

|Shape| S/A Formula|Volume Formula
Cube | S.A=6s^2 | V=s^3
Sphere|S.A+4 pi r^2|V=4/3 pi r^3
Cylinder| S.A=2 pi r^2+2 pi rh |V= pi r^2 h

i need help with this i only have the answer for cube but the other ones i don’t understand

To find and simplify the volume-to-surface-area ratio for each of the three possible ice cube shapes, we will substitute the formulas for surface area (S/A) and volume (V) into the given chart.

1. Cube:
Surface area formula: S.A = 6s^2
Volume formula: V = s^3

Volume-to-surface-area ratio for a cube:
V/S.A = (s^3)/(6s^2)

Simplifying the ratio:
V/S.A = s/6

2. Sphere:
Surface area formula: S.A = 4πr^2
Volume formula: V = (4/3)πr^3

Volume-to-surface-area ratio for a sphere:
V/S.A = ((4/3)πr^3)/(4πr^2)

Simplifying the ratio:
V/S.A = (r/3)

3. Cylinder:
Surface area formula: S.A = 2πr^2 + 2πrh
Volume formula: V = πr^2h

Volume-to-surface-area ratio for a cylinder:
V/S.A = (πr^2h)/(2πr^2 + 2πrh)

Simplifying the ratio:
V/S.A = (rh)/(2r + h)

To find and simplify the volume-to-surface-area ratio for each of the three possible ice cube shapes (cube, sphere, and cylinder), we can use the respective formulas for surface area (S/A) and volume (V) provided in the chart.

1. Cube:
Surface Area Formula (S/A) for a cube: S.A = 6s^2, where s represents the length of each side of the cube.
Volume Formula (V) for a cube: V = s^3.

To find the volume-to-surface-area ratio for a cube, we need to divide the volume of the cube by its surface area:

V/S.A = (s^3) / (6s^2).

To simplify this ratio, we can cancel out the common factor of s:

V/S.A = s^2 / 6.

2. Sphere:
Surface Area Formula (S/A) for a sphere: S.A = 4πr^2, where r represents the radius of the sphere.
Volume Formula (V) for a sphere: V = (4/3)πr^3.

To find the volume-to-surface-area ratio for a sphere, we need to divide the volume of the sphere by its surface area:

V/S.A = ((4/3)πr^3) / (4πr^2).

To simplify this ratio, we can cancel out the common factors of 4 and πr^2:

V/S.A = (1/3)r / 1.

The simplified volume-to-surface-area ratio for a sphere is:

V/S.A = 1/3r.

3. Cylinder:
Surface Area Formula (S/A) for a cylinder: S.A = 2πr^2 + 2πrh, where r represents the radius of the base and h represents the height of the cylinder.
Volume Formula (V) for a cylinder: V = πr^2h.

To find the volume-to-surface-area ratio for a cylinder, we need to divide the volume of the cylinder by its surface area:

V/S.A = (πr^2h) / (2πr^2 + 2πrh).

To simplify this ratio, we can cancel out the common factor of πr:

V/S.A = (h) / (2 + 2h).

The simplified volume-to-surface-area ratio for a cylinder is:

V/S.A = h / (2 + 2h).

These are the simplified volume-to-surface-area ratios for each of the three possible ice cube shapes.

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