Final answer:
To find the volume of the sink basin modeled as a hemisphere, you need to find the radius first and then use the volume formula for a sphere.
Step-by-step explanation:
To find the volume of the sink basin, we need to model it as a hemisphere. The circumference of the sink basin is given as 91 3/4 inches. Using the formula for the circumference of a hemisphere, which is C = 2πr, where C is the circumference and r is the radius, we can find the radius of the sink basin.
First, convert the given circumference to decimal form: 91 3/4 inches = 91.75 inches.
Then, solve the equation C = 2πr for r: r = C/(2π) = 91.75/(2 × 3.1415) ≈ 14.6106 inches.
The radius of the sink basin is approximately 14.6106 inches. Now, we can use the formula for the volume of a sphere, which is V = (4/3)πr³, where V is the volume and r is the radius, to find the volume of the sink basin.
Substituting the value of the radius into the formula: V = (4/3)π(14.6106)³ ≈ 11563.062 cubic inches.