Question

A​ marble-top bathroom sink has the shape of a hemispherical​ (a half-sphere) porcelain bowl with an inside diameter of 18 in. How much​ water, in​ gallons, will the bowl​ hold?

Answer 1

Calculate the volume of a hemisphere using the radius from the diameter provided, and convert this volume from cubic inches to gallons to determine the sink's water capacity.

Step-by-step explanation:

To calculate the amount of water a hemispherical sink will hold, we need to find the volume of the hemisphere and then convert that volume to gallons. First, we find the radius of the sink by dividing the diameter by two, which gives us a radius of 9 inches.

The formula for the volume of a hemisphere is ½ × (4/3)πr³, so we plug in our radius to get the volume in cubic inches. After determining the volume, we convert cubic inches to gallons knowing that 1 gallon is approximately 231 cubic inches.

Volume in gallons = Volume in cubic inches / 231 cubic inches/gallon

Volume in gallons ≈ 381.97 cubic inches / 231 cubic inches/gallon

Volume in gallons ≈ 1.65 gallons

Therefore, the marble-top bathroom sink can hold approximately 1.65 gallons of water.

Answer 2

The correct answer is 6.61 gallons.

Step-by-step explanation:

A​ marble-top bathroom sink has the shape of a hemispherical​ (a half-sphere) porcelain bowl with an inside diameter of 18 inches.

Radius of the hemisphere is 9 inches.

Volume of hemisphere is
`(2)/(3)` × π ×
`r^(3)` =
`(44)/(21)` ×
`9^(3)` = 1527.4285 cubic inches.

Also 1 cubic inches = 0.004329 gallons

⇒ 1527.4285 cubic inches = 1527.4285 × 0.004329 = 6.61 gallons.

Thus the bowl can hold 6.61 gallons of water.