A semi-circular swimming pool with a radius of 3.5m and a depth of 4m is to be filled with water. Calculate the volume of water needed. Also, if 30 men can complete a job in 6 days working 12 hours a

The radius ($r$) of the semi-circular pool is $3.5 \text{ m}$.
The depth ($h$) of the pool is given as $4 \text{ m}$.

Area of semi-circle = $\frac{1}{2} \pi r^2$
Using $\pi \approx \frac{22}{7}$:

Volume = Area of base $\times$ depth

The volume of water in the pool is $\boxed{77 \text{ m}^3}$.

5a)

Total work units = Number of men $\times$ Hours per day $\times$ Number of days

Let $M_2 = 16 \text{ men}$, $H_2 = 9 \text{ hours/day}$.
Total work units = $M_2 \times H_2 \times D_2$

Longer time = $D_2 - D_1$

It will take $\boxed{9 \text{ days longer}}$.

5b) i)

Principal ($P$) = $500,000 \text{ frs}$
Interest rate ($R$) = $5\%$ per annum = 0.05
Time ($T$) = $2\frac{1}{2}$ years = $2.5 \text{ years}$

$I = P \times R \times T$.

The interest Mr. Olia will have to pay is $\boxed{62,500 \text{ frs}}$.

5b) ii)

Doh will receive.
Total amount = Principal + Interest

Mr. Doh will receive $\boxed{562,500 \text{ frs}}$ from Mr. Olia at the end of the period.

6a)

• Tax: $25 \text{ frs}$ per $1,000 \text{ frs}$ of income. Annual income = $3,000,000 \text{ frs}$. Tax rate = $\frac{25}{1000} = 0.025$. Annual tax = $0.025 \times 3,000,000 \text{ frs} = 75,000 \text{ frs}$.
• Food: $50,000 \text{ frs}$ per month. Annual food cost = $50,000 \text{ frs/month} \times 12 \text{ months} = 600,000 \text{ frs}$.
• Monthly house rent: $80,000 \text{ frs}$ per month. Annual rent = $80,000 \text{ frs/month} \times 12 \text{ months} = 960,000 \text{ frs}$.
• Clothing and cosmetics: $250,000 \text{ frs}$ per annum.
• Health care and transport: $100,000 \text{ frs}$ for the year.
• Miscellaneous: $76,000 \text{ frs}$ annually.

Total annual expenditure = Tax + Food + Rent + Clothing/Cosmetics + Health/Transport + Miscellaneous

Her annual expenditure is $\boxed{2,061,000 \text{ frs}}$.