We have responses from Penny and Stephen La Rocque.

All three of these problems involve finding the volume of a cylinder. The volume of a cylinder is given by

V = r^{2} h

where r is the radius and h is the height. One Imperial gallon is 277.42 cubic inches so for problem 1 I would convert all the units to inches before finding the volume. 4 ft is 4 12 = 48 inches so the height is 48 inches and the radius is ^{16}/_{2} = 8 inches so volume of the boiler is

V = r^{2} h = 8^{2} 48 = 9650.97 cubic inches.

Since there are 277.42 cubic inches in an Imperial gallon the boiler will hold

^{9650.97}/_{277.42} = 34.79 gallons.

If you wanted US gallons you would divide by 231 rather than 277.42 since there are 231 cubic inches in a US gallon.

I can't solve problem 2 since I don't know the density of the material in the pipe or the thickness of the pipe wall.

Problem 3 again involves the volume of a cylinder. I know tat a litre is 1000 cu cm so I would convert the measurements to cm before finding the volume. One meter is 100 centimeters so the tank is 400 cm in diameter and hence the radius is 200 cm, and the height is 600 cm. Thus the volume is

V = r^{2} h = 200^{2} 600 = 75398223.7 cu cm

which is

^{75398223.7}/_{1000} = 75398.2 litres.

I hope this helps,

Penny

> 1.A range boiler is 16 in. in diameter and 4 ft high.How many gallons will it hold ?

This shape is a cylinder. The volume of a cylinder is calculated by the formula

V = pi r^{2} h, where pi is about 3.1416, r is the radius of the cylinder (half the

diameter) and h is the height (or length if it is lying on its side). Of course, you must first change the radius and the height to be the same units (in this case, probably you'd want to change the radius from 8 inches to 2/3 feet). When you use the formula, you get a volume in cubic feet. This is a volume measurement which you can convert to other volume measurements by multiplying by an appropriate conversion factor.

According to my references, there are 6.23 imperial gallons in a cubic foot or 7.48 american gallons in a cubic foot.

> 2.What would the weight in Kg be if the pipe was .4 of a meter in diameter and it was 8.6 m in length

I'm not sure what you want to weigh: the pipe itself, some liquid filling the pipe, or the two together - and there isn't enough information in the question to answer any of these, I'm afraid. Again, this is a cylinder shape, so we can use the calculation method above to find the volume of the (interior of the) pipe. If we assume that the diameter is the inside diameter and that the question is asking for the weight in Kg of water that fills the pipe, then we can make the following calculation:

V = pi (0.2)^{2} 8.6

which gives us the volume in meters^{3}. Since water is 1000 Kg/m^{3}, just multiply by 1000 to get the Kg.

If the question is asking something about the weight of the pipe, you'd need to know at least the thickness of the pipe and its density (aka. specific gravity) to solve the question.

> 3. An oil storage tank is 4 m in diameter and 6 m high..How many liters of oil can be stored

This is another cylinder. Calculate the volume in the same manner as the above questions, then convert to liters using the conversion factor 1000 liters = 1 m^{3}.

Good luck when you write your ticket!

Stephen La Rocque>