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Answer :
Final answer:
To find the volume of the sink basin, use the formula V = (4/3)πr³. Divide the circumference by 2π to find the radius. Plug the radius into the volume formula to calculate the volume of the sink basin.
Explanation:
To find the volume of the sink basin, you can use the formula for the volume of a sphere. The formula is V = (4/3)πr³, where V is the volume and r is the radius. In this case, the sink basin is modeled as a hemisphere, so the radius is half of the circumference. Given that the circumference is 913 inches, you can find the radius by dividing it by 2π. Once you have the radius, you can plug it into the volume formula to calculate the volume of the sink basin in cubic inches.
First, find the radius: r = circumference / 2π = 913 / (2 × 3.14) ≈ 145.85 inches
Then, calculate the volume: V = (4/3)πr³ = (4/3) × 3.14 × (145.85)³ ≈ 817,829.5 cubic inches
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Final answer:
To find the volume of the sink's basin modeled as a hemisphere, we use the formulas for circumference and volume of a hemisphere. By substituting the given circumference into the circumference formula, we can find the radius. Using the radius, we then calculate the volume using the volume formula for a hemisphere.
Explanation:
To find the volume of the sink's basin, we can use the formula for the volume of a hemisphere: V = (2/3) * π * r^3, where r is the radius of the hemisphere. Given that the circumference of the sink is 913 inches, we can calculate the radius using the formula for circumference: C = 2πr. Rearranging the formula, we find r = C / (2π), which gives us r = 913 / (2π) ≈ 145.3 inches. Substituting this value into the volume formula, we get V = (2/3) * π * (145.3)^3 ≈ 682,399.4 cubic inches.
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