Volume Of Cylinders & Cones
Hi there. This math post is on volume of cylinders and cones. We first start with a review of finding area of circles before moving on to volume of cylinders and cones.
As usual, math text rendered with QuickLaTeX.com
Topics
- Review - Area Of Circles
- Volume Of Cylinders
- Volume Of Cones
- Answers To Practice Problems
Review - Area Of Circles
Before getting into the volume of cylinders, it is important to review the area of circles.
Given a radius length of a circle (halfway from the middle to a circle's boundary point), we can compute the circle's area as:
where pi is a famous irrational number that is 3.14 when rounded to two digits and r is is the radius length.
As a side note, Pi is the ratio of the circumference of the circle divided by the circle's diameter.
Volume Of Cylinders
A cylinder has two flat circles and a vertical height. Computing the volume of a cylinder is not too hard once you use the idea of multiplying the area of the circle by the (vertical) height of the cylinder (represented by h).
Example
What is the volume of a tomato can if the radius of the circle base is 5 centimetres and the can has a height of 10 centimetres?
From the question, the radius and the height values are given. Just simply substitute the values accordingly and compute the volume.
Practice Problems - Volume Of Cylinders
Determine the volume of a cylinder with a circle radius of 2 metres and a cylinder height of 8 metres.
Given a circle radius of pi and a cylinder height of 111 centimetres, what is the volume of this cylinder?
What is the radius of a circle where the cylinder height is 10 centimetres and the cylinder volume is 490 pi cubic centimetres?
Volume Of Cones
With computing the volume of cones, think of it as taking the volume of its "cylinder" and dividing by three.
The derivation/proof of the volume of a cone formula is way beyond middle school maths. It requires Calculus II integration (volume of revolution) from university/college mathematics. My memory on integration for volumes of revolution is rusty so here is a link for the proof if you are interested.
Note that I am not going over the case where the Pythagorean Theorem is used to find the vertical height of a cone.
Practice Problems - Volume Of Cones
An ice cream cone has a circle radius of 5 centimetres and a vertical height of 15 centimetres. What is the volume of this ice cream cone?
The volume of this one cone is 1000 cubic centimetres with a cone vertical height of 30 centimetres. What is the circle's radius?
Answers To Practice Problems
Volume Of Cylinders
32Pi cubic metres
111 pi cubed cubic centimetres
7 centimetres
Volume Of Cones
125 Pi cubic centimetres
10 centimetres
