Volume of Cylinder and Sphere

Cylinder 1

V=

A cylinder is a solid that has two parallel faces which are congruent circles. These faces form the bases of the cylinder. The cylinder has one curved surface. The height of the cylinder is the perpendicular distance between the two bases.

The volume of a cylinder is given by the formula:Volume = Area of base × height

where r = radius of cylinder and h is the height or length of cylinder.

How to remember: Volume = pizza Imagine you just cooked a pizza.

The radius is "z", and the thickness "a" is the same everywhere ... what is the volume?

Answer: pi × z × z × a

(we would normally write "pi" as π, and z × z as z2, but you get the idea!)

Z

Cylinder 2

Volume of hollow cylinder: = πR2 h – πr2 h= πh (R2– r2)Example:A hollow cylinder copper pipe is 21cm long. Its outer and inner diameters are 10cm and 6cm respectively. Find the volume of copper used in making the pipe.Solution:Given that: Height of cylindrical pipe, h=21cm=210cm∴ External radius, R==5cm Internal radius, R==3cm Volume of the copper used in making the pipe = Volume of external cylinder − volume of internal cylinder =πh−π=π()h=227[52−32]×210 =227×16×210=22×16×30=10560

Cylinder 3-Horizontal cylinder segment

So as a formula the volume of a horizontal cylindrical segment is Where Volume=sl

s = the area of the circle segment forming the end of the solid, and l = the length of the cylinder.The area of the circle segment can be found using it's height and the radius of the circle . 

S= where:C is the central angle in DEGREESR is the radius of the circle of which the segment is a part.π is Pi, approximately 3.142sin is the trigonometry Sine function.

Cylinder 4A cylindrical segment (truncated cylinder) is the solid cut from a circular cylinder by two planes. A common special case is given by one of these planes being perpendicular to the axis of the cylinder (the base of the cylinder) and the other plane being tilted without cutting the base of the cylinder.

The volume V of the truncated cylinder is given by

V = r2π(h1+h2)/2

Sphere

To find a sphere's volume, the amount of space inside a three-dimensional

object, we use this formula:

𝑉=43𝜋 𝑟3