The problem is written in Malay and translates to the following:

Question: An open cylinder at the top has a height twice the radius of its base. It is filled with water until three-quarters full. An additional 539 mL of water is needed to completely fill the cylinder. Calculate the surface area of the cylinder in square centimeters (cm²). (Use $\pi = \frac{22}{7}$).

Steps to solve:

1. Understand the Cylinder Geometry:

   • The cylinder has an open top, so the surface area will consist of the base area and the lateral surface area.
   • Let $r$ be the radius of the base, and the height of the cylinder is $2r$ (as given).

2. Volume Calculation:

   • The total volume of the cylinder is $V_{\text{total}} = \pi r^2 h = \pi r^2 \cdot 2r = 2\pi r^3$.
   • Initially, the cylinder is filled to three-quarters, so $V_{\text{filled}} = \frac{3}{4} \times 2\pi r^3 = \frac{3\pi r^3}{2}$.

   When an additional 539 mL of water is added, the cylinder is completely full. Hence, the difference in volume is 539 mL, which is equivalent to 539 cm³.

   Therefore, the equation is: $V_{\text{total}} - V_{\text{filled}} = 539$ Substituting the volumes: $2\pi r^3 - \frac{3\pi r^3}{2} = 539$ Simplify the left-hand side: $\frac{\pi r^3}{2} = 539$ Substituting $\pi = \frac{22}{7}$: $\frac{\frac{22}{7} r^3}{2} = 539$ Simplify further: $\frac{11 r^3}{7} = 539$ Multiply both sides by 7: $11 r^3 = 539 \times 7 = 3773$ Divide by 11: $r^3 = \frac{3773}{11} = 343$ Taking the cube root of both sides: $r = \sqrt[3]{343} = 7 \, \text{cm}$

3. Calculate Surface Area:

   • The surface area of the open cylinder is the sum of the lateral area and the base area.
   • Lateral surface area $A_{\text{lateral}} = 2\pi r h = 2\pi r \cdot 2r = 4\pi r^2$.
   • Base area $A_{\text{base}} = \pi r^2$.
   • Total surface area $A_{\text{total}} = A_{\text{lateral}} + A_{\text{base}} = 4\pi r^2 + \pi r^2 = 5\pi r^2$.

   Substituting $r = 7$ cm and $\pi = \frac{22}{7}$: $A_{\text{total}} = 5 \times \frac{22}{7} \times 7^2 = 5 \times \frac{22}{7} \times 49$ Simplify: $A_{\text{total}} = 5 \times 22 \times 7 = 770 \, \text{cm}^2$

Thus, the surface area of the cylinder is 770 cm².

Would you like a detailed explanation of any step or have additional questions?

Related Questions:

1. How do you calculate the lateral surface area of a closed cylinder?
2. What is the formula for the volume of a cylinder?
3. How does changing the height of a cylinder affect its surface area?
4. How can you derive the formula for the surface area of an open cylinder?
5. If the radius is doubled, how will the surface area change?

Tip: Always double-check unit conversions (e.g., milliliters to cubic centimeters) when working with volumes.