SOLUTION: A cylindrical hot water tank has an outside diameter of 0.4 yards and a height of 1.2 yards. It's outside is to be completely covered with an insulating material which is 1.2 inche

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Question 367095: A cylindrical hot water tank has an outside diameter of 0.4 yards and a height of 1.2 yards. It's outside is to be completely covered with an insulating material which is 1.2 inches thick. Calculate the volume of the insulating material required.
I found lateral surface area of 1.507964474. area of bottom of 0.125663706 for a total area of 1.63362818. Do I need to compensate for the top too? Where do I go next to get the volume of material? Thank you in advance for any help!
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A cylindrical hot water tank has an outside diameter of 0.4 yards and a height of 1.2 yards. It's outside is to be completely covered with an insulating material which is 1.2 inches thick. Calculate the volume of the insulating material required.
I found lateral surface area of 1.507964474. area of bottom of 0.125663706 for a total area of 1.63362818. Do I need to compensate for the top too? Where do I go next to get the volume of material?
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The diameter of the top and the bottom of the tank is (0.4*36) = 14.4 inches
The area of top of the tank is (pi)7.2^2 = 162.86in^2
The height of the tank is (1.2*36) = 43.2 in
The Volume of the tank is (162.86*43.2) = 7035.55 in^3
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The diameter of the top and bottom insulation is (14.4+2*1.2) = 16.8 inches
The area of the top and of the bottom is (pi)8.4^2 = 221.67 in^2
The height of the tank with the insulation cover is (43.2+2*1.2) = 45.6 inches
The Volume of the covered tank cylinder is (221.67*45.6) = 10108.15 in^3
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The Vol of the insulation is 10108.15-7035.55 = 3072.59 in^3 = 1.7781 yrd^3
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Cheers,
Stan H.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you do not need lateral area to solve this.

you need volume only.

the basic idea is to take the volume of the cylinder with the insulation and subtract from that the volume of the cylinder without the insulation.

the difference is the volume of the insulation.

the tank has an outside diameter of .4 yards and a height of 1.2 yards.

the thickness of the insulation material is 1.2 inches.

this increases the diameter of the cylinder by 2.4 inches (1.2 inches on each opposite side).

this also increases the height of the cylinder by 2.4 inches (1.2 inches on each top or bottom).

2.4 inches is equivalent to 2.4 / 12 / 3 = .0666666667 yards.

you need to add this to the diameter of the cylinder and to the height of the cylinder.

the diameter of the cylinder increases to .46666666667 yards with the width of the insulation added.

the height of the cylinder increases to 1.2666666667 yards with the width of the insulation added./

the formula for volume of a cylinder is equal to pi * r^2 * h.

r is the radius and h is the height.

the radius of the cylinder is equal to 1/2 the diameter.

1/2 the diameter of .4 yards is equal to .2 yards.

1/2 the diameter of .46666666667 yards is equal to .2333333333 yards.

the volume of the cylinder without the insulation is equal to pi * .2^2 * 1.2 which equals .048 * pi.

the volume of the cylinder with the insulation is equal to pi * .233333333^2 * 1.2666666667 yards which equals .068962963 * pi.

the volume of the insulation is equal to the volume of the cylinder with the insulation minus the volume of the cylinder without the insulation.

the volume of the insulation is therefore equal to .068962963 minus .048 which equals .020962963 * pi cubic yards.

multiply this by pi to get .065857091 cubic yards.

multiply this by 36^3 to get 3072.628417 cubic inches.

if you wanted to solve this by inches to start with, you would have done the following:

height of the tank without insulation is 1.2 yards * 3 * 12 = 43.2 inches.

diameter of the tank without insulation is .4 yards * 3 * 12 = 14.4 inches.

the height of the tank with insulation is 43.2 inches + (2*1.2) inches which equals a total of 45.6 inches.

the diameter of the tank with insulation is 14.4 inches + (2*1.2) inches which equals a total of 16.8 inches.

the radius of the tank is equal to 1/2 the diameter of the tank.

the radius of the tank without insulation is equal to 14.4 / 2 = 7.2 inches.

the radius of the tank with insulation is equal to 16.8 / 2 = 8.4 inches.

the volume of the tank without the insulation is equal to pi * 7.2^2 * 43.2 which equals pi * 2239.488 cubic inches.

the volume of the tank with the insulation is equal to pi * 8.4^2 * 45.6 which equals pi * 3217.536 cubic inches.

the volume of the insulation is the volume of the tank with the insulation minus the volume of the tank without the insulation.

this equals pi * 2239.488 cubic inches subtracted from pi * 3217.536 cubic inches which equals pi * 978.048 cubic inches.

if you multiply this by pi, you get an answe4r of 3072.628412 cubic inches.

if you divide this by 36^2, you get an answer of .06585709 cubic yards.

the answer you get if you convert everything to yards is the same answer that you get if you convert everything to inches.

it's just a matter of preference which way you want to go.