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?
2006-09-01 10:46:55 · 6 answers · asked by Olivia 4 in Science & Mathematics ➔ Mathematics
d = 8ft
Ltotal = 24
Lcylinder = 24 - 2r = 24 - d = 16ft
Vcylinder = (16)(pi)4^2 = approx. 804
V(2hemispheres) = (4/3)(pi)4^3 = approx 268
Vtotal = 1072 cu ft
2006-09-01 10:54:00 · answer #1 · answered by zot 2 · 0⤊ 0⤋
The tank has hemispherical heads.
Each head could be combined to make a sphere with a radius of 4 ft.
The total length of the tank is 24 ft. You must subtract the two hemispheres to get a cylinder 16 ft long with an 4 ft radius.
The volume of the two combined hemispheres can be found using the following form
V=4/3*pi*r^3
V=4/3*3.14*4^3=268 ft^3
The volume of the cylinder can be found using the form
V=l*pi*r^2=16*3.14*4^2=804 ft^3
The total volume should be 804+268=1,072 ft^3
It is important to remember that the internal volume is 1,072 ft^3, but the tanks capacity is a number dictated by design and safety constraints and may be 871 ft^3 which is the number you are trying to arrive at.
2006-09-01 18:18:47 · answer #2 · answered by Scott S 4 · 1⤊ 0⤋
2 ends:
Volume of a sphere is 4/3 pi r^3 - each side would be half a sphere, but there are 2 ends so the formula will work.
4/3 pi (4)^3 = Approx 85.33 pi
Now for the cylinder - total length is 24 ft, but each end is 4 ft of lenght, making the cylinder 16 ft. Volume of a cylinder pi r^2 h, or
pi (4)^2 (16) = 256 pi
Add the 2 together for 341.33 pi, or approx 1071.78 cubic feet.
2006-09-01 17:56:48 · answer #3 · answered by p_rutherford2003 5 · 0⤊ 0⤋
I get 1072 ft^3. An exact answer would be 4^5*pi/3.
Think of it as the two ends make a sphere of radius 4, and in the middle is a cylinder of radius 4 and height 16. So the sphere is (4/3)*pi*r^3 and the cylinder is pi*r^2*h.
2006-09-01 17:53:24 · answer #4 · answered by zandyandi 4 · 1⤊ 0⤋
Volume of the cylindrical part= pi x r ^2 x height
= 3.14 x 16 x 16 (the height is 24 - 4 -4, right)
=803.84
+ volume of the hemispheres
= I forget, is it 4/3 pi r^3?
=4/3 x 3.14 x 64
=267.88
804 + 268 = 1072
But I could be wrong for the sphere formula
2006-09-01 18:01:35 · answer #5 · answered by Goddess of Grammar 7 · 0⤊ 0⤋
Area = pi (r^2) = 3.14 * 4^2 = 3.14 * 16 = 50.24
Volume = Area * height = 50.24 * 24 = 1205.76
Hemisphere = 1/2 Volume = 602.88 CU FT
I think?
2006-09-01 17:51:37 · answer #6 · answered by RobRetz 2 · 0⤊ 0⤋