## 2013/08/03

### Formula Math Of Cylinder

Label:
Formula Math

Mathematics formula math of Cylinder :

Definition of

**A cylinder**as a solid figure that is bound by a curved surface and two flat surfaces. The surface area of a cylinder can be found by breaking it down into 2 parts:
1. The two circles that make up the caps of the
cylinder.

2. The side of the cylinder, which when "unrolled" is a rectangle.

2. The side of the cylinder, which when "unrolled" is a rectangle.

Formula
Math :

The area of each end cap can be found from the radius r of the circle, which is given by:

Thus the total area of the caps is 2πr

The area of a rectangle is given by:

The width is the height

Thus the rectangle's area is rewritten as:

Combining these parts together we will have the total surface area of a cylinder, and the final formula is given by:

The area of each end cap can be found from the radius r of the circle, which is given by:

*A = πr*^{2}Thus the total area of the caps is 2πr

^{2}.The area of a rectangle is given by:

*A = height × width*The width is the height

*h*of the cylinder, and the length is the distance around the end circles, or in other words the perimeter/circumference of the base/top circle and is given by:*P = 2πr*Thus the rectangle's area is rewritten as:

*A = 2πr × h*Combining these parts together we will have the total surface area of a cylinder, and the final formula is given by:

*A = 2πr*^{2}+ 2πrh
Smart
Math Formula Note :

By factoring 2πr from each term we can simplify the formula to:

The lateral surface area of a cylinder is simply given by:

Smart Math Formula in the application :

Surface Area = 175.84 cm

**π**= Pi, approximately 3.142,**r**= the radius of the cylinder,**h**= height of the cylinderBy factoring 2πr from each term we can simplify the formula to:

*A = 2πr(r + h)*The lateral surface area of a cylinder is simply given by:

*LSA = 2πr × h*.Smart Math Formula in the application :

- Find the surface area of a cylinder with a radius of 4 cm, and a height of 3 cm.

**Smart Solution:***SA = 2 × π × r*^{2}+ 2 × π × r × h*SA = 2 × 3.14 × 4*^{2}+ 2 × 3.14 × 4 × 3*SA = 6.28 × 16 + 6.28 × 12**SA = 100.48 + 75.36**SA = 175.84*Surface Area = 175.84 cm

^{2}- Find the surface area of the cylinder with a radius of 5.5cm and height of 10cm.

**Smart Solution:**The radius of cylinder = 5.5 cm.

The height of cylinder = 10 cm.

The total surface area of the cylinder is therefore:

*TSA = 2πr(r+h)*

*TSA = 11π (5.5+10)*

*TSA = 170.5 π*

*TSA = 535.6 cm*

^{2}- Find the total surface area of a cylindrical tin of radius 17 cm and height 3 cm.

**Smart Solution:**Again as in the previous example:

*TSA = 2πr(r+h)*

*TSA = 2π× 17(17+3)*

*TSA = 2π×17×20*

*TSA = 2136.56 cm*

^{2}- Find the surface area of the cylinder with radius of 6 cm and height of 9 cm.

**Smart Solution:**The radius of cylinder:

*r = 6 cm*

The height of cylinder:

*h = 9 cm*

Total surface area of cylinder is therefore:

*TSA = 2πr(r + h)*

*TSA = 12π (6+9)*

*TSA = 180 π*

*TSA = 565.56 cm*

^{2}-
Find the radius of cylinder whose
lateral surface area is 150 cm
^{2}and its height is 9 cm.

**Smart Solution:**Lateral surface area of cylinder is given by:

*LSA = 2πrh*

Given that:

*LSA = 150cm*

^{2}*h = 9cm*

π is the constant and its value = 3.14

Substitute the values in the formula and find the value of r by isolating it from the equation:

*LSA = 2πrh*

150 = 2

*× π × r × 9*

*r = 150 / (2×9× π)*

*r = 2.65cm*

So the radius of the cylinder is 2.65 cm.

That is Smart Math aplication from Cylinder Formula Math.

## 0 komentar

## Post a Comment