A propane tank is in the form of a right, circular cylinder with hemispherical ends. The diameter of the cylinder is 8 feet and the total length of the tank, including the ends, is 24 feet. Correct to the nearest whole cubic foot, what is the volume of the tank?
2007-01-27 03:10:44 · 9 answers · asked by chris 2 in Science & Mathematics ➔ Mathematics
The two hemispherical ends can be combined into a sphere. Use the formula for a sphere's volume.
4/3 • π • r³ = 4/3 • 3.14 • 64 = 267.947 cubic feet
The remaining flat-ended cylinder can be solved using the appropriate formula for the volume of a cylinder.
π • r² • height = 3.14 * 16 * (24-8) [tank length minus sphere diameter = length of flat cylinder]
π • 16 • (16)
π • 256 = 803.84 cubic feet.
Add the two.
267.947+803.84= 1071.787, round up to 1072.
Tada!
2007-01-27 03:16:09 · answer #1 · answered by Anonymous · 3⤊ 1⤋
Volume of a cylinder with hemispherical ends
D = 8
L cylinder - ends = 16 (24 - 8)
Volume of a cylinder:
Pi r^2 h
3.141593 * 4^2 * 16 = 804.2477193
Volume of a sphere:
(Pi/6)d3
0.52359 * 8^3 = 268.0825731
804.2477193
268.0825731
= 1072.00 to nearest ft^3
2007-01-27 03:34:35 · answer #2 · answered by Anonymous · 2⤊ 0⤋
So it is equal to a sphere 8 ft in diameter (both ends) and a cylinder 8 ft dia and 16 ft long.
4/3 PI r3 for sphere (4 / 3) * Pi * (4^3) = 268.082573
PI r2 L for cylinder 16 * Pi * (4^2) = 804.247719
1072 yup
2007-01-27 03:22:43 · answer #3 · answered by Mike1942f 7 · 3⤊ 0⤋
Ends of tank make a 8' dia. sphere, center of tank is a 8' X 16' cylinder.
8'sphere (4'radius) = (4/3) X pi X (4x4x4) = 268.08
8 X 16 cylinder (4' radius) = pi X (4x4) X 16 = 804.24
Answer = 1072 C.F.
2007-01-27 03:27:20 · answer #4 · answered by Eddie M. 3 · 2⤊ 0⤋
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2016-05-24 05:18:04 · answer #5 · answered by Anonymous · 0⤊ 0⤋
Assume that the ends are exactly 1/2 of a sphere of diameter 8 feet therefore the cylinder portion is only 16 feet.
The volume of a sphere is
(4/3)pi(D/2)^3 = (4/3)(3.14159)(64)=268.082
The volume of the cylinder is
pi(D/2)^2 x L = (3.14159)(16)(16) = 804.247
The total estimate volume = 268.082+804.247=1072.322
2007-01-27 03:23:59 · answer #6 · answered by lostlatinlover 3 · 3⤊ 0⤋
Circular Cylinder formula
V = π r² h
Sphere formula
V = 4/3 π r³
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The problem mentions circular cylinder Tank. There is no mention of a sphere.
- - - - - - - - - - -s-
2007-01-27 06:18:39 · answer #7 · answered by SAMUEL D 7 · 0⤊ 1⤋
Yes, 1072 seems to be correct.
2007-01-27 03:16:27 · answer #8 · answered by Anonymous · 3⤊ 0⤋
That is a good number.
Here is a good link I use once and a while.
http://grapevine.abe.msstate.edu/~fto/tools/vol/
2007-01-27 03:37:52 · answer #9 · answered by dyke_in_heat 4 · 0⤊ 1⤋