Question

The volume of a soap bubble is 2,225 mm cubed . Find the radius and diameter of the soap bubble. Use 3.14 for pi.

Answer 1

Answers:

radius = 8.10004 mm

diameter = 16.20008 mm

Each value is approximate. Round them however needed.

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Work Shown

r = radius, d = diameter, V = volume of sphere

V = (4/3)*pi*r^3

2225 = (4/3)*3.14*r^3

2225 = 4.18667*r^3

r^3 = 2225/4.18667

r^3 = 531.44862

r = cube root of 531.44862

r = 531.44862^(1/3)

r = 8.10004 mm

d = 2*r = 2*8.10004 = 16.20008 mm

Answer 2

Answer:

radius: 8.1 mm

diameter: 16.2 mm

Step-by-step explanation:

The volume ($V$) of a sphere is given by the formula:

$V = \dfrac{4}{3} \pi r^3$

where

• $r$ is the radius of the sphere.

Given that the volume of the soap bubble is $2,225 \, \textsf{mm}^3$ and using the value of $\pi$ as $3.14$, we can set up the equation:

$2,225 = \dfrac{4}{3} \times 3.14 \times r^3$

Now, let's solve for $r$:

$r^3 = \dfrac{2,225 \times 3}{4 \times 3.14}$

$r^3 = \dfrac{6,675}{12.56}$

$r^3 \approx 531.4490446$

Now, take the cube root of both sides to find $r$:

$r \approx \sqrt[3]{531.4490446}$

$r \approx 8.100040871 \, \textsf{mm}$

$r \approx 8.1\, \textsf{mm ( in nearest tenth)}$

So, the radius of the soap bubble is approximately $8.1 \, \textsf{mm}$.

Now, to find the diameter ($d$), we simply multiply the radius by 2:

$d = 2 \times r$

$d \approx 2 \times 8.1$

$d \approx 16.2 \, \textsf{mm}$

So, the diameter of the soap bubble is approximately $16.2 \, \textsf{mm}$.