Answer :
We start with the formula for the volume of a sphere:
[tex]$$
V = \frac{4}{3} \pi r^3
$$[/tex]
Given that the volume is [tex]$V = 100.5 \text{ cm}^3$[/tex], we set up the equation:
[tex]$$
100.5 = \frac{4}{3} \pi r^3
$$[/tex]
To solve for [tex]$r$[/tex], isolate [tex]$r^3$[/tex] by multiplying both sides by [tex]$\frac{3}{4\pi}$[/tex]:
[tex]$$
r^3 = \frac{3 \times 100.5}{4\pi}
$$[/tex]
Calculating the numerator:
[tex]$$
3 \times 100.5 = 301.5
$$[/tex]
So, we have:
[tex]$$
r^3 = \frac{301.5}{4\pi}
$$[/tex]
Next, divide the numerator by [tex]$4\pi$[/tex]:
[tex]$$
\frac{301.5}{4\pi} \approx \frac{301.5}{12.566370614359172} \approx 23.992607671103222
$$[/tex]
Now, take the cube root of both sides to solve for [tex]$r$[/tex]:
[tex]$$
r = \sqrt[3]{23.992607671103222} \approx 2.884202955114811
$$[/tex]
Finally, rounding [tex]$r$[/tex] to the nearest whole number gives:
[tex]$$
r \approx 3 \text{ cm}
$$[/tex]
Thus, the radius of the sphere is [tex]$\boxed{3\text{ cm}}$[/tex].
[tex]$$
V = \frac{4}{3} \pi r^3
$$[/tex]
Given that the volume is [tex]$V = 100.5 \text{ cm}^3$[/tex], we set up the equation:
[tex]$$
100.5 = \frac{4}{3} \pi r^3
$$[/tex]
To solve for [tex]$r$[/tex], isolate [tex]$r^3$[/tex] by multiplying both sides by [tex]$\frac{3}{4\pi}$[/tex]:
[tex]$$
r^3 = \frac{3 \times 100.5}{4\pi}
$$[/tex]
Calculating the numerator:
[tex]$$
3 \times 100.5 = 301.5
$$[/tex]
So, we have:
[tex]$$
r^3 = \frac{301.5}{4\pi}
$$[/tex]
Next, divide the numerator by [tex]$4\pi$[/tex]:
[tex]$$
\frac{301.5}{4\pi} \approx \frac{301.5}{12.566370614359172} \approx 23.992607671103222
$$[/tex]
Now, take the cube root of both sides to solve for [tex]$r$[/tex]:
[tex]$$
r = \sqrt[3]{23.992607671103222} \approx 2.884202955114811
$$[/tex]
Finally, rounding [tex]$r$[/tex] to the nearest whole number gives:
[tex]$$
r \approx 3 \text{ cm}
$$[/tex]
Thus, the radius of the sphere is [tex]$\boxed{3\text{ cm}}$[/tex].
