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Answer :
To find the volume of sand a cylindrical container can hold in gallons, calculate the cylinder's volume and convert from cubic inches to gallons. The container has a height of 10 inches, a diameter of 12 inches, and it holds approximately 5 gallons of sand.
The question involves calculating the volume of sand in gallons that a cylindrical container can hold when it is filled to build a sandcastle. The container has a height of 10 inches and a diameter of 12 inches. To find the volume of the cylinder, we use the formula for the volume of a cylinder, V = πr²h, where r is the radius of the cylinder and h is its height. The radius, being half of the diameter, is 6 inches. So, the volume is calculated as V = π(6 inches)²(10 inches). This gives a volume of approximately 1,130.97 cubic inches. Since there are 231 cubic inches in one gallon, we divide the total volume of sand by this number to determine the volume in gallons, resulting in approximately 4.9 gallons. Rounding to the nearest gallon, the container holds about 5 gallons of sand.
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Answer:
5 gallons
Step-by-step explanation:
The container volume can be found from the formula for the volume of a cylinder:
V = πr^2h
V = π(6 in)^2(10 in) = 360π in^3 ≈ 1130.97 in^3
Then the number of gallons is ...
(1130.97 in^3)/(231 in^3/gal) = 4.896 gal
The approximate volume of sand is 5 gallons.
