4.2 If the cost of galvanized steel for the tanks is R320 per square metre, how much will the cylindrical water tank cost to produce?

To calculate the cost of producing a cylindrical water tank, we need to know the dimensions of the tank. Let's assume the cylindrical water tank has a radius of \( r \) meters and a height of \( h \) meters. The surface area of a cylindrical tank can be calculated using the formula: \[ A = 2\pi r^2 + 2\pi rh \] Given that the cost of galvanized steel for the tanks is R320 per square meter, the total cost of producing the cylindrical water tank can be calculated by multiplying the surface area by the cost per square meter: \[ \text{Total Cost} = A \times \text{Cost per Square Meter} \] Let's calculate the total cost of producing the cylindrical water tank. Simplify the expression by following steps: - step0: Solution: \(2\pi r^{2}+2\pi rh\) - step1: Reorder the terms: \(2\pi r^{2}+2\pi hr\) The surface area of the cylindrical water tank is given by \( 2\pi r^2 + 2\pi rh \). Now, we can calculate the total cost of producing the cylindrical water tank by multiplying the surface area by the cost per square meter (R320). Let's proceed with the calculation. Simplify the expression by following steps: - step0: Solution: \(\left(2\pi r^{2}+2\pi rh\right)\times 320\) - step1: Reorder the terms: \(\left(2\pi r^{2}+2\pi hr\right)\times 320\) - step2: Multiply the terms: \(320\left(2\pi r^{2}+2\pi hr\right)\) - step3: Multiply the expression: \(640\pi \left(r^{2}+hr\right)\) - step4: Rearrange the terms: \(640\pi r^{2}+640\pi hr\) The total cost of producing the cylindrical water tank is \( 640\pi r^2 + 640\pi rh \) in Rands. Therefore, the cost to produce the cylindrical water tank will depend on the values of the radius \( r \) and the height \( h \) of the tank.