To determine the volume of helium that a spherical weather balloon can hold given its diameter of 10 feet, follow these steps:
1. Determine the Radius:
The radius of a sphere is half of its diameter. Given the diameter is 10 feet, we divide by 2 to find the radius.
[tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{10 \text{ feet}}{2} = 5 \text{ feet}
\][/tex]
2. Formula for the Volume of a Sphere:
The volume [tex]\( V \)[/tex] of a sphere can be calculated using the formula:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
where [tex]\( r \)[/tex] is the radius of the sphere.
3. Substitute the Radius into the Formula:
With the radius [tex]\( r \)[/tex] being 5 feet, we substitute this value into the volume formula.
[tex]\[
V = \frac{4}{3} \pi (5^3)
\][/tex]
4. Calculate the Value of [tex]\( 5^3 \)[/tex]:
First, compute [tex]\( 5^3 \)[/tex], which is 5 multiplied by itself three times.
[tex]\[
5^3 = 5 \times 5 \times 5 = 125
\][/tex]
5. Substitute and Multiply:
Substitute 125 into the volume formula and multiply:
[tex]\[
V = \frac{4}{3} \pi \times 125
\][/tex]
6. Final Calculation:
Multiply [tex]\( \frac{4}{3} \pi \)[/tex] and 125 to get the volume.
[tex]\[
V \approx 523.5987755982989 \text{ cubic feet}
\][/tex]
Thus, the weather balloon holds approximately 523.6 cubic feet of helium.
