Question 4: Find the number of liters of water required to fill the swimming pool.

The swimming pool has a trapezoidal cross-section. To calculate its volume:

1. Find the area of the trapezoidal cross-section:

   • Height $h = 3 \, \text{m}$
   • Bases: $b_1 = 5 \, \text{m}$, $b_2 = 1 \, \text{m}$
   • Area of the trapezoid: $A = \frac{1}{2} \cdot (b_1 + b_2) \cdot h = \frac{1}{2} \cdot (5 + 1) \cdot 3 = 9 \, \text{m}^2$

2. Calculate the volume of the pool:

   • Length $l = 20 \, \text{m}$
   • Volume: $V = A \cdot l = 9 \cdot 20 = 180 \, \text{m}^3$

3. Convert to liters:

   • 1 cubic meter = 1000 liters.
   • Volume in liters: $180 \cdot 1000 = 180,000 \, \text{liters}$

Answer for Question 4:

The pool requires 180,000 liters of water.

Question 5: A sphere has a surface area of $100 \, \text{cm}^2$.

a) Find its radius:

The surface area of a sphere is given by: $A = 4 \pi r^2$

1. Rearrange for $r^2$: $r^2 = \frac{A}{4 \pi}$
2. Substituting $A = 100 \, \text{cm}^2$: $r^2 = \frac{100}{4 \pi} = \frac{100}{12.5664} \approx 7.9577$
3. Solve for $r$: $r = \sqrt{7.9577} \approx 2.8 \, \text{cm}$

b) Find its volume:

The volume of a sphere is given by: $V = \frac{4}{3} \pi r^3$

1. Substituting $r \approx 2.8$: $V = \frac{4}{3} \pi (2.8)^3 = \frac{4}{3} \cdot 3.1416 \cdot 21.952 \approx 91.6 \, \text{cm}^3$

Answer for Question 5:

a) Radius: 2.8 cm
b) Volume: 91.6 cm³

Let me know if you need further clarifications!

Here are 5 related questions for practice:

1. What is the formula for the volume of a cylinder, and how would it compare to the pool's shape?
2. If the trapezoid's dimensions change to $b_1 = 6 \, \text{m}$, $b_2 = 2 \, \text{m}$, and $h = 4 \, \text{m}$, what would the new volume of the pool be?
3. How does the surface area formula of a sphere relate to its radius?
4. What would the radius of a sphere with a volume of $200 \, \text{cm}^3$ be?
5. How much water would be required to fill a hemispherical tank with a radius of $2.5 \, \text{m}$?

Tip: Always double-check unit conversions, especially between cubic meters and liters.