A water tank has an outside diameter of 412cm and an inside diameter of 410cm.
The internal height of the tank is 200cm and the external height is 205cm.
a. What volume of water (in cm3'square') can the tank hold when full?
b. What is the volume of material used in the tank?
2007-06-18 15:52:19 · 5 answers · asked by ebneter_chick 1 in Science & Mathematics ➔ Mathematics
I assume this is a cylindrical tank. The volume it can hold is based on the inside dimensions.
The diameter of one end is 410cm, so the radius is 205cm. The volume of a cylinder is base * height; the base is a circle with radius 205cm, so the area is pi * r^2 = 42025pi. That base times the height of 200cm = 8405000pi cubic cm = 8.405pi cubic meters (around 26.405 cubic meters) as the inside volume.
By similar calculation, the outside volume is 8.69938pi cubic meters (about 27.330 cubic meters). The volume of the material used in the tank itself is the difference between the two: 8.69938pi - 8.405pi = .29438pi cubic meters (about .925 cubic meters).
Hope that helps.
2007-06-18 16:03:20 · answer #1 · answered by Tim P. 5 · 0⤊ 0⤋
Finding volumber for a cylinder ( this is the shape of the tank)
pi * radius^2 * height
a. Volume of water the tank holds would have to be the internal volume.
Therefore:
Internal radius = diameter/2 = 205cm
Internal height = 200cm
= pi * radius^2 * height ( radius is diameter/2)
= 22/7 * 205^2 * 200
= 3.14 * 42,025 * 200
= 26,415,714.29 cm^3
answer = 26,415,714.29 cm^3
b. Volume of material used
= external volume of tank subtract internal volume of tank ( this would give you the material in between.
External diameter = 412cm
External height = 205
radius = 412/2 = 206
External volume = pi * radius^2 * height
= 22/7 * 206^2 * 205
= 3.14 * 42,436 * 205
=27,340,908.57cm^3
External Volume = 27,340,908.57cm^3
Internal volume was 26,415,714.29 cm^3
Volume of material used in tank =
External volume - internal volume
= 27,340,908.57cm^3 - 26,415,714.29 cm^3
= 925,194.2814cm^3
Answer = 925,194.2814cm^3
a = 26,415,714.29 cm^3
b = 925,194.2814cm^3
2007-06-18 16:44:29 · answer #2 · answered by Addie 1 · 0⤊ 0⤋
a)
Volume of water = Ï.r².h
r = 205 cm
h = 200 cm
V = Ï x 205² x 200 cm³
V = 26,405,086 cm³
b)
External volume = Ve
Ve = Ï x 206² x 205 cm³
Ve = 27,329,908 cm³
Volume of material = Ve - V
Volume of material = 924,822 cm³ (to nearest cm³)
2007-06-19 07:49:25 · answer #3 · answered by Como 7 · 0⤊ 0⤋
410*200
2007-06-18 15:55:16 · answer #4 · answered by Anonymous · 0⤊ 1⤋
Why do math if school is almost out?
2007-06-18 15:54:54 · answer #5 · answered by Anonymous · 0⤊ 2⤋