LPG (liquedfied petroleum gas) is stored in highly insulated spherical vessels in most oil refineries. If the inside diameter of one of these tanks is 11.4ft, find it's volume. Report your answer to the nearest one-tenth of a gal use (pie)=3.14, and 1 cubic ft =7.5 gal.
a. 5,815.1 gal
b. 48,968.9 gal
c. 12,242.2 gal
d. 726.9 gal
i want to say my answer is d
diameter = 11.4, so
radius = 5.7 ft
V = (4/3)π (r^3)
= (4/3)π (5.7)^3 = 775.7346 cubic feet
but 1 cu ft = 7.5 gal, so .....
sure looks like a) to me
To find the volume of the spherical vessel, we can use the formula for the volume of a sphere:
V = (4/3) * π * r^3,
where V is the volume, π (pi) is approximately 3.14, and r is the radius of the sphere.
First, we need to find the radius of the sphere, which is half the diameter. In this case, the diameter is given as 11.4ft, so the radius can be calculated as:
r = 11.4ft / 2 = 5.7ft.
Now, we can substitute the radius value into the volume formula:
V = (4/3) * 3.14 * (5.7ft)^3.
Calculating the volume:
V ≈ (4/3) * 3.14 * (5.7ft)^3 ≈ 48,968.9 cubic feet.
However, the question asks for the answer in gallons, so we need to convert cubic feet to gallons. Since 1 cubic foot is equal to 7.5 gallons:
Volume in gallons = 48,968.9 cubic feet * 7.5 gallons/cubic foot.
Calculating the volume in gallons:
Volume in gallons ≈ 48,968.9 cubic feet * 7.5 gallons/cubic foot ≈ 367,266.8 gallons.
Rounding to the nearest one-tenth of a gallon:
Volume ≈ 367,266.8 gallons ≈ 367,260.0 gallons.
Therefore, the answer to the nearest one-tenth of a gallon is:
b. 48,968.9 gallons.