Can you clarify when to half the diameter when finding volume of cylinder? I had the following problem:
1. Picture of cylinder with base of 48cm (no dotted lines) and height of 7cm.
I thought i would solve by using V = 3.14(24)^2 (7) = 12,660.5 cubic meters.
According to the teacher's answer sheet, the correct answer is 336 cubic meters using V = Bh or 48(7).
Do I consider taking half of the base only if it's represented by dotted lines?
V = pi*r^2*h = 3.14*24^2*7 = 12,660.5 cm^3(Not m^3).
V = B*h, B=Area of the base, V=pi*r^2*h
48 is not the area of the base; it is the diameter of the base.
Diameter*height = Square units.
Diameter/2 = Radius. So you take 1/2 of
the diameter to get the radius.
I hope this helps.
Correction: In your case, 48 is the
area of the base:
V = B*h = 48m^2 * 7m = 336 m^3 or 336 cubic meters.
Again, take half of the base only when it is the diameter.
When finding the volume of a cylinder, you do not need to halve the diameter. The formula for the volume of a cylinder is V = Bh, where B represents the base area and h represents the height. In your case, the base of the cylinder is given as 48 cm, so the correct calculation would be V = 48(7), which equals 336 cubic centimeters.
It seems like you used the formula for the area of a circle (A = πr^2) instead of the formula for the volume of a cylinder. In your calculation, you correctly found the area of the circular base by squaring the radius (24 cm) and multiplying by π. However, to find the volume of the cylinder, you need to multiply the area of the base by the height.
In general, you only need to halve the diameter if you are calculating the radius of a circle. For example, if the problem asked you to find the radius of the cylinder's base given a diameter of 48 cm, you would divide the diameter by 2 to get the radius (24 cm). But when finding the volume, you don't need to halve the diameter; you just need to use the correct formula for the volume of a cylinder.