Final answer:
The radius of the soap bubble is approximately 8.72 mm, and the diameter is approximately 17.44 mm. This is calculated by using the volume formula for a sphere.
Step-by-step explanation:
The problem asks us to find the radius and diameter of a soap bubble, given its volume. The formula for the volume of a sphere, which is the shape of a soap bubble, is V = ⅓πr3.
To solve for the radius, r, we can rearrange the formula to r = ∛(V / (⅓π)). Plugging in the given volume of the soap bubble, 3155 mm3, and using 3.14 for π, we get:
r = ∛(3155 / (⅓π))
r = ∛(3155 / (4.19))
r = ∛(752.98)
r ≈ 8.72 mm (approximately)
The diameter, d, of the soap bubble is simply twice the radius: d = 2r. Therefore, the diameter is approximately 17.44 mm.