Sphere Volume
1. The problem: Calculate the volume of a sphere given its radius.
2. The formula for the volume of a sphere is $$V=\frac{4}{3}\pi r^{3}$$ where $r$ is the radius.
3. Calculate volumes for each radius:
1. $r=2.2m$:
$$V=\frac{4}{3}\pi (2.2)^{3}=\frac{4}{3}\pi (10.648)=\frac{4}{3}\times 3.1416 \times 10.648 \approx 44.602 m^{3}$$
2. $r=1.1cm$:
$$V=\frac{4}{3}\pi (1.1)^{3}=\frac{4}{3}\pi (1.331)=\frac{4}{3}\times 3.1416 \times 1.331 \approx 5.575 cm^{3}$$
3. $r=5cm$:
$$V=\frac{4}{3}\pi (5)^{3}=\frac{4}{3}\pi (125)=\frac{4}{3}\times 3.1416 \times 125 \approx 523.599 cm^{3}$$
4. $r=6m$:
$$V=\frac{4}{3}\pi (6)^{3}=\frac{4}{3}\pi (216)=\frac{4}{3}\times 3.1416 \times 216 \approx 904.779 m^{3}$$
5. $r=2.5dm$:
$$V=\frac{4}{3}\pi (2.5)^{3}=\frac{4}{3}\pi (15.625)=\frac{4}{3}\times 3.1416 \times 15.625 \approx 65.45 dm^{3}$$
Final answers with units:
1. Volume = $44.602 m^{3}$
2. Volume = $5.575 cm^{3}$
3. Volume = $523.599 cm^{3}$
4. Volume = $904.779 m^{3}$
5. Volume = $65.45 dm^{3}$