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There are 231 cubic inches in a gallon. A large juice can has a diameter of 6 inches and a height of 10 inches. How many gallons of juice does the can hold? Round your answer to the nearest tenth.

Answer :

Answer: Juice Can can hold up to 1.22 gallon of Juice


Step-by-step explanation:

We are given that a large juice can has a diameter of 6 inches and has a height of 10 inches

we need to find how many gallons of juice does the can hold

Please see a "can" has a cylindrical figure

so here we can find the volume of juice that the given "can" holds using the formula for Volume of cylinder

Volume of cylinder is given by :

[tex]V=\pi r^2h[/tex]

we know that height h = 10 inches , diameter d = 6 inches so radius would be r = 6/2 = 3 inches

now plugging the value of h = 10 and r = 3 in the formula for volume of cylinder , we get:

[tex]V=\pi (3)^2(10)[/tex]

[tex]V=\pi (9)(10)[/tex]

so V=282.74 cubic inches

Now we need to find the volume in terms of gallon

so we will convert 282.74 cubic inches to gallon

Known fact :

231 cubic inches = 1 gallon

so , 1 cubic inches = 1/231 gallon

and 282.74 cubic inches = (1/231)*(282.74) gallon

Hence, Volume in gallons = 1.22 gallon



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Rewritten by : Barada

Final answer:

The large juice can with a 6-inch diameter and a 10-inch height holds approximately 1.2 gallons of juice, rounded to the nearest tenth.

Explanation:

To find out how many gallons of juice the can holds, we need to calculate its volume in cubic inches and then convert that volume to gallons. The formula for the volume of a cylinder is Volume = πr^2h, where π is approximately 3.14159, r is the radius of the base of the cylinder, and h is the height of the cylinder.

First, we find the radius of the can by dividing the diameter by 2. The diameter is 6 inches, so the radius is 3 inches. Then we use the formula to calculate the volume:
Volume = 3.14159 × (3 inches)^2 × 10 inches = 282.74 cubic inches.

Now we know the volume in cubic inches, and to convert to gallons, we use the conversion 1 gallon = 231 cubic inches. Therefore, we divide the volume by 231:
282.74 cubic inches ÷ 231 cubic inches/gallon ≈ 1.2 gallons.

So, the can holds approximately 1.2 gallons of juice, rounded to the nearest tenth.