Question

1. calculate the length of the basin sink.

a. find the surface area of the sink. round your answer to two decimal places.
hint: the surface area of the sink = total cost of the sink / cost per square centimeter.
b. using the surface area calculated above, find the length (h) of the cylindrical section of the sink. round your answer to two decimal places.
remember: sa_cylinder = 2πrh (rectangular part) and sa_sphere = 4πr²
hint: solve for h in the diagram. notice that the surface area of the sink includes two quarter spheres and half a cylinder.

Explanation:

Step1: Calculate surface area of sink

Let the total cost of the sink be $C$ and cost per square - centimeter be $c$. Then the surface area $A$ of the sink is given by the formula $A=\frac{C}{c}$. Since we are not given the values of $C$ and $c$, we'll assume we have calculated $A$ as a result of this step.

Step2: Analyze surface - area components of sink

The surface area of the sink consists of two quarter - spheres (which is equivalent to half a sphere) and half a cylinder. The surface area of half a sphere is $SA_{half - sphere}=2\pi r^{2}$, and the surface area of half a cylinder is $SA_{half - cylinder}=\pi rh$. So the total surface area $A = 2\pi r^{2}+\pi rh$.

Step3: Solve for $h$

We can re - arrange the formula $A = 2\pi r^{2}+\pi rh$ to solve for $h$. First, subtract $2\pi r^{2}$ from both sides: $A - 2\pi r^{2}=\pi rh$. Then, divide both sides by $\pi r$ to get $h=\frac{A - 2\pi r^{2}}{\pi r}$.

Answer:

a. Surface area $A=\frac{\text{total cost of the sink}}{\text{cost per square centimeter}}$ (after substituting the actual values of total cost and cost per square centimeter and rounding to two decimal places).
b. $h=\frac{A - 2\pi r^{2}}{\pi r}$ (after substituting the value of $A$ calculated in part a and the value of $r$, and rounding to two decimal places).