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.
l = 2×21 = 42 cm
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: Find surface area of sink

Since the surface area formula given is $SA=\text{total cost of the sink}/\text{cost per square centimeter}$, but the total cost of the sink and cost per square - centimeter are not provided in the problem description. So, we assume we have found the surface area $SA$ in part (a).

Step2: Set up surface - area formula for the 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 $2\pi r^{2}$ and the surface area of half a cylinder is $\pi rh$. So, $SA = 2\pi r^{2}+\pi rh$.

Step3: Solve for $h$

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

Answer:

Since the values of $SA$ and $r$ are not given in the problem, the formula for the length of the cylindrical section of the sink is $h=\frac{SA - 2\pi r^{2}}{\pi r}$