Answer :
To find the radius of a ball with a given volume, we start with the formula for the volume of a sphere:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Given:
[tex]\[ V = 14.5 \, \text{m}^3 \][/tex]
[tex]\[ \pi = 3.14 \][/tex]
First, we rearrange the formula to solve for the radius [tex]\( r \)[/tex]:
[tex]\[ r^3 = \frac{3V}{4\pi} \][/tex]
Substitute the known values into the equation:
[tex]\[ r^3 = \frac{3 \times 14.5}{4 \times 3.14} \][/tex]
Calculate the numerator:
[tex]\[ 3 \times 14.5 = 43.5 \][/tex]
Calculate the denominator:
[tex]\[ 4 \times 3.14 = 12.56 \][/tex]
Now, divide the numerator by the denominator:
[tex]\[ r^3 = \frac{43.5}{12.56} \approx 3.463375796178344 \][/tex]
Next, to find the radius [tex]\( r \)[/tex], we take the cube root of both sides:
[tex]\[ r \approx \sqrt[3]{3.463375796178344} \approx 1.512980065164049 \, \text{m} \][/tex]
Finally, we round the radius to the nearest tenth:
[tex]\[ r \approx 1.5 \, \text{m} \][/tex]
So, the radius of the ball is:
[tex]\[ \boxed{1.5} \, \text{m} \][/tex]
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Given:
[tex]\[ V = 14.5 \, \text{m}^3 \][/tex]
[tex]\[ \pi = 3.14 \][/tex]
First, we rearrange the formula to solve for the radius [tex]\( r \)[/tex]:
[tex]\[ r^3 = \frac{3V}{4\pi} \][/tex]
Substitute the known values into the equation:
[tex]\[ r^3 = \frac{3 \times 14.5}{4 \times 3.14} \][/tex]
Calculate the numerator:
[tex]\[ 3 \times 14.5 = 43.5 \][/tex]
Calculate the denominator:
[tex]\[ 4 \times 3.14 = 12.56 \][/tex]
Now, divide the numerator by the denominator:
[tex]\[ r^3 = \frac{43.5}{12.56} \approx 3.463375796178344 \][/tex]
Next, to find the radius [tex]\( r \)[/tex], we take the cube root of both sides:
[tex]\[ r \approx \sqrt[3]{3.463375796178344} \approx 1.512980065164049 \, \text{m} \][/tex]
Finally, we round the radius to the nearest tenth:
[tex]\[ r \approx 1.5 \, \text{m} \][/tex]
So, the radius of the ball is:
[tex]\[ \boxed{1.5} \, \text{m} \][/tex]
