1. Stating the problem: We need to calculate three things: - The volume of a hemisphere with diameter 4 m. - The time to fill a hemisphere tank of radius 4 m at a pipe flow rate of 0.25 m³/s, given in minutes. - The surface area of a sphere of radius 4 m. 2. Calculate the volume of the hemisphere: - Diameter $d=4$ m, so radius $r=\frac{d}{2}=2$ m. - Volume of a full sphere is $V_{sphere} = \frac{4}{3}\pi r^3$. - Volume of a hemisphere is half that: $V_{hemisphere} = \frac{1}{2} \times \frac{4}{3}\pi r^3 = \frac{2}{3} \pi r^3$. - Substitute $r=2$: $$V=\frac{2}{3} \pi (2)^3 = \frac{2}{3} \pi \times 8 = \frac{16}{3} \pi \approx 16.755$$ cubic meters. 3. Calculate the time to fill the tank: - Flow rate = 0.25 m³/s. - Time to fill $= \frac{Volume}{flow rate} = \frac{16.755}{0.25} = 67.02$ seconds. - Convert to minutes: $\frac{67.02}{60} \approx 1.117$ minutes. - Correct to 3 significant figures: $1.12$ minutes. 4. Calculate the surface area of the sphere: - Surface area for sphere: $A=4\pi r^2$. - Substitute $r=4$ m (note radius is 4 m as per problem second and third part): $$A=4 \pi (4)^2=4 \pi \times 16=64 \pi \approx 201.062$$ square meters. Final answers: - Volume of hemisphere (radius 2 m): $16.755$ cubic meters. - Time to fill hemisphere tank (radius 4 m) at 0.25 m³/s: $1.12$ minutes. - Surface area of sphere (radius 4 m): $201.062$ square meters.