Cylinder
A cylinder is a solid object having curved surface with
two circular faces of same size. Measuring jars, circular pillars, circular
pipes, gluesticks etc. are some examples of cylinder. A cylinder is also called
a circular prism. The figure given below is a cylinder.
Where,
AX = BY = r = radius of cylinder
AB = XY = h = height of cylinder
XY = axis of cylinder
********************
10 Math Problems officially announces the release of Quick Math Solver and 10 Math Problems, Apps on Google Play Store for students around the world.
********************
********************
If the axis of cylinder is perpendicular to the circular
base then the cylinder is called a right circular cylinder, otherwise it is
called an oblique cylinder.
Net of right circular cylinder
Formula for surface area and volume of right circular cylinder
Curved surface area (CSA) of cylinder = 2πrh
Total surface area (TSA) of cylinder = 2πr(r + h)
Volume of cylinder = πr2h
Hollow Cylinder
A hollow cylinder is a solid bounded by two co-axial
cylinders of the same height and different radii. For example - water pipe,
rubber pipe etc. The figure given below is a hollow cylinder where R is
external radius and r is the internal radius.
i. Area of base ring = πR2 – πr2
= π(R2 – r2)
ii. Curved surface area of hollow cylinder =
External surface + Internal surface
= 2πRh + 2πrh
= 2πh(R + r)
iii. Total surface area of hollow cylinder =
Curved surface area + 2 Area of base ring
= 2πh(R+r) + 2π(R2–r2)
= 2πh(R+r) + 2 π(R+r) (R–r)
= 2π(R+r) (h+R–r)
iv. Volume of the material used in hollow
cylinder = External volume – internal volume
= πR2h – πr2h
= πh(R2 – r2)
You can comment your questions or problems
regarding cylinder here.
0 comments: