Smart

## 2013/08/13

### Formula Math Perimeter of a Circle

Perimeter is the distance around a closed figure and is typically measured in millimetres (mm), centimetres (cm), metres (m) and kilometres (km). These units are related as follows:
10 mm = 1 cm
100 cm = 1 m
1000 m = 1 km

The word 'perimeter' is also sometimes used instead of circumference.
If we know the radius
Given the radius of a circle, the circumference or perimeter can be calculated using the formula bwloe:

Perimeter (P) = 2 · π · R
where: R is the radius of the circle π is Pi, approximately 3.142
If we know the diameter
If we know the diameter of a circle, the circumference can be found using the formula
Perimeter (P) = π · D
where: D is the diameter of the circle π is Pi, approximately 3.142
If we know the area
If we know the area of a circle, the circumference can be found using the formula:
Perimeter (P) = √(4 · π · A )
where: A is the area of the circle π is Pi, approximately 3.142

Smart Math Example 1:
A circular flower-bed has a radius of 9 m. Find the perimeter/circumference of the flower-bed.
Smart Solution:

P = 2 · π · R
P = 2 · 3.1416 · 9
P = 56.5487 cm
So, the perimeter/circumference of the flower-bed is 56.5487 m.

Smath Math Example 2: Find the perimeter of the given circle whose diameter is 4.4 cm.
Smart Solution:
Given that:
Diameter of the circle (D) = 4.4 cm.

We know the formula to find the perimeter of the circle if the diameter is given, namely π·D.

Substitute the diameter 4.4 and Pi value as 3.14 in the above formula.
Perimeter = (3.14)(4.4) = 13.82
Therefore 13.82 cm is the perimeter of the given circle.

Smart Math Example 3: If the radius is 11.7 cm. Find perimeters (circumference) of the circle.
Smart Solution:
Given that:
Radius (r) = 11.7cm
Perimeter (circumference) of circle P = 2 π r
Substitute the r value in the formula, we have:

P = 2 x 3.14 x 11.7
P = 79.56 cm
Thus, the perimeter of the circle is 79.56cm

Smart Math Example 4: Find the perimeter and area of the circle, if the radius of the circle is 8cm.
Smart Solution: We have given the radius, which is 8cm. So, by using the formula of the perimeter of the circle, we have:

P = 2πr
P = 2×3.14×8
P = 50.24 cm
And for the area of the circle:-
A = π r2
A = 3.14×(8)2
A = 200.96cm2

Smart Math Example 5: The wheel of a bullock cart has a radius of 6 m. If the wheel rotates once how much distance does the cart move?
Smart Solution:
If the wheel rotates once, the cart will move by a distance equal to the perimeter of the wheel.
Step 1:
P = 2πr
P = 2× 3.14× 6 = 37.68 m
Thus, the bullock cart moves 37.68 m in one revolution of the wheel.

That is Formula Math Perimeter of a Circle

### Formula Math Perimeter of a Rectangle

Formula Math in rectangle, the distance around the outside of the rectangle is known as perimeter. A rectangle is 2-dimensional; however, perimeter is 1-dimensional and is measured in linear units such as feet or meter etc.The perimeter of a rectangle is the total length of all the four sides.
Perimeter of rectangle = 2L + 2W.
Math Example 1 : Rectangle has the length 13 cm and width 8 cm. solve for perimeter of rectangle.
Smart Solution:
Given that:
Length (l) = 13 cm
Width (w) = 8 cm

Perimeter of the rectangle = 2(l + w) units
P = 2(13 + 8)
P = 2 (21)
P = 42

Thus, the perimeter of the rectangle is 42 cm.

Math Example 2: If a rectangle's length is 2x + 1 and its width is 2x – 1. If its area is 15 cm2, what are the rectangle's dimensions and what is its perimeter?

Smart Solution:
We know that the dimensions of the rectangle in terms of x:
l = 2x + 1
w = 2x – 1

Since the area of a rectangle is given by:
A = l * w

We can substitute the expressions for length and width into the equation for area in order to determine the value of x.

A = l * w
15 = (2x + 1) (2x -1)
15 = 4x2 – 1
16 = 4x2
x = ±2

Note that the value of x must be positive and therefore in our case, the value of x is 2. And now we have:
l = 5 cm
w = 3 cm
Therefore, the dimensions are 5cm and 3cm.

Now, substituting these values in the formula for perimeter, we will get
P = 2l + 2w
P = 2(5)+2(3)
P = 10+6
P = 16 cm

Math Example 3: Find the area and the perimeter of a rectangle whose length is 24 m and width is 12m?
Smart Solution:
Given that:
length = L = 24m
width = W = 12m

Area of a rectangle:
A = L × W
A = 24 × 12
A = 188 m2

Perimeter of a rectangle:
P = 2L + 2W
P = 2(24) + 2(12)
P = 48 + 24
P = 72 m

Math Example 4: Find the area and perimeter of a rectangle whose breadth is 4 cm and the height 3 cm.
Smart Solution:
Area = b×h = 4×3 = 12 cm2.
Perimeter = 2(b) + 2(h) = 2(4) + 2(3) = 8 + 6 = 14.

Math Example 5: Calculate the perimeter of the rectangle whose length is 18cm and breadth 7cm
Smart Solution:
Given that:
L = 18 cm
B = 7 cm

Perimeter of rectangle = 2(length + breadth)
P = 2 (L + B)
P = 2 (18 + 7)
P = 50 cm

Math Example 6: Find the perimeter of rectangle whose length is 6 inches and width is 4 inches.
Smart Solution:
P = 2(L + B)
P = 2(6 + 4)
P = 20 in

Math Example 7: A boy walks 5 times around a park. If the size of the park is 100m by 50m, find the distance the boy has walked. If he walks 100m in 5 minutes, how long will it take for him in total?
Smart Solution:
Given that:
Length = L = 100m
Width = W = 50m
Rounds = 5
Time per 100m = 5minutes.

Perimeter of the park:
P = 2 L + 2 W.
P = 2 × 100 + 2 × 50
P = 200 + 100
P = 300 m

Total distance walked = 5 × Perimeter of the park.
= 5 × 300
= 1500 meters

Total time taken = Total distance walked × time taken to walk 1m.
= 1500 × 5/100
= 75 minutes or 1hr 15minutes

That is smart math formula of Perimeter of a Rectangle

## 2013/08/04

### Formula Math Surface Area of a Sphere

Difinition smart math formula of A sphere is a three-dimensional space, such as the shape of a football. A sphere is a body bounded by a surface whose every point is equidistant (i.e. the same distance) from a fixed point, called the centre or the origin of the sphere.
Like a circle in three dimensions, all points from the center are constant. The distance from the center to any points on boundary is known as the radius of the sphere. The maximum straight distance through the sphere is known as the diameter of the sphere. One-half of a sphere is called a hemisphere.

We can find the total surface area of a sphere by using the following formula:
SA = 4 π r2
where r is the radius.

NOTE: The value of π can never be calculated exactly, so the surface area of a sphere is only a approximation.

Surface area of sphere in terms of diameter = πd2

where d is the diameter of the sphere.

•   What is the total surface area of a sphere whose radius is 5.5 meters?

Smart Solution:
Given that:
r =5.5
Surface area of the sphere:
SA = 4 × π × r2
SA = 4 × π × (5.5)2
SA = 4 × 3.14 × 30.25
SA = 379.94
Thus the surface area of the sphere is 379.94 m2.

A spherical ball has a surface area of 2464 cm2. Find the radius of the ball, correct to 2 decimal places, using π = 3.142.

Smart Solution:
SA = 4 × π × r2
In order to find r, we need to isolate it from the equation above:
r2 = SA / (4π)
r2 =2464 / (4 × π)
r2 =196.054
r = √(196.054)
r = 14.00 cm

•   Find the surface area of the sphere whose radius is 18 cm. [π = 3.14]

Smart Solution:
r = 18 cm
The surface area of a sphere is given by:
SA = 4 × π × r2
SA = 4 × π × 182
SA = 4 × π × 342
SA = 4069.44 cm2

The surface area of the sphere is 4069.44 cm2.

• Find the surface area of a sphere, whose radius is given as r = 11 cm.

Smart Solution:
The formula for calculating the surface area of sphere is given by:
SA = 4 × π × r2
SA = 4 × 3.14 × 112
SA = 1519.76
The surface area of sphere is 1519.76 cm2.

Example 5: A hemisphere has the radius measured to 8.3 cm. Find the surface area of it without the base.
Solution:
r = 8.3 cm
The surface area of a hemisphere without the base is determined by using the following formula math:

SA = 2 × π × r2
SA = 2 × π × 8.32
SA = 432.62
The surface area of the hemisphere is therefore 432.62 cm2.

•   Find the surface area of a sphere whose radius is 6cm?

Smart Solution:
SA = 4 × π × r2
SA = 4 × π × 62
SA = 4 × π × 36
SA = 452cm2

That is formula math in aplication mathematics of  Formula Math Surface Area of a Sphere.

## 2013/08/03

### Formula Math Volume of a Cuboid

Smart Math formula Volume of a Cuboid

In geometry, a cuboid is a solid shaped figure formed by six faces. There are two definitions for a cuboid. In the more general definition of a cuboid, the only supplementary condition is that each of these six faces is a quadrilateral. Otherwise, the word “cuboid” is sometimes used for referring a shape of this type in which each of the faces is a rectangle, and in which each pair of adjacent faces meets in a right angle.

A cuboid with length l units, width w units and height h units has a volume of V cubic units given by: V = l × w × h
•   A jewellery box that has the shape of a rectangular prism, has a height of 13 cm, a length of 35 cm and a width of 22cm. Find the volume of the jewellery box?
Math Solution:
V = l × w × h
V= 13 × 35 × 22

V= 10010 cm3
•   Find the volume of a brick whose size is 30 cm by 25 cm by 10 cm.
Math Solution:
The volume of the brick is given by:
V = l × w × h
V = 30 × 25 × 10
V = 7500 cm3

So, the volume of the brick is 7500cm3.

•   Calculate the volume of a cuboid whose size is 8cm × 12cm × 6cm
Math Solution:
Volume of the cuboid is given by:
V = l × w × h
V = 8 × 12 × 6
V = 576 cm3
• Given that the dimension of a cuboidal shape beam is 10m in length, 60 cm in width and 25 cm in thickness. How much does Nick have to pay for it, if it costs \$250.00/ m3?
Math Solution:
Notice that all the measurements should be expressed in the same units (100 cm = 1 m). Volume of the beam = length x breadth x height (thickness here)
V = 10 x (60/100) x (25/100) = 1.5 m3
The final price of the beam will be: 1.5 x 250 = \$375.00.
•   A goods wagon shaped in the form of cuboid of measure 60m × 40m × 30m. How many cuboidal boxes can be stored in it if the volume of one box is 0.8 cubic meters.
Math Solution:
The volume of one box = 0.8 m3
The volume of the goods wagon is: 60 × 40 × 30 = 72000 m3
Number of boxes that can be stored in the goods wagon is therefore:
72000 / 0.8 = 90000
Hence the number of cuboidal boxes that can be stored in the goods wagon is 90,000.
•   Find the height of a cuboid whose volume is 300 cubic cm and the base area is 30cm.
Math Solution:
V = l × w × h
Since the base area is defined as: l × w, the height is therefore:
h = V / base area
h = 300 / 30
h = 10 cm
•   A box of the size 60 cm × 40 cm × 30 cm. If the size of one chocolate bar is 24 cm × 12 cm × 4 cm each, how many bars can the box hold?
Math Solution:
The volume of the box = 60 × 40 × 30 = 72000 cm3
The volume of each bar = 24 × 12 × 4 = 1152 cm3

Therefore the number of chocolate bars that the box can hold is:
72000/1152 = 62
•  The surface areas of the three coterminous faces of a cuboid are 6, 15 and 10 cm2 respectively. Find the volume of the cuboid.
Math Solution:
To begin with we need to determine the length, width and height of the cuboid.
l = √(6)
w = √(15)
h = √(10)

V = l × w × h
V = √(6) × √(15) × √(10)
V = 30 cm2

### Surface Area of a Cuboid Formula Math

The total surface area (TSA) of a cuboid is the sum of the areas of its 6 faces,
which is given by:

TSA = 2 (lw + wh + hl)
Remember the surface area is the total area of all the faces of a 3D shape.
The lateral surface area of a cuboid is given by:
LSA = 2 (lh + wh) = 2 h (l + w)

Smart Math Formula in aplication :
Find the total surface area of a cuboid with dimensions 8 cm by 6 cm by 5 cm.

TSA = 2 (lw + wh + hl)
TSA = 2 (8*6 + 6*5 + 5*8)
TSA = 2 (48 + 30 + 40)
TSA = 236
So, the total surface area of this cuboid is 236 cm2.
Find the surface area of a cuboid of dimensions 4.8 cm, 3.4 cm and 7.2 cm.

Math Solution:
Area of Face 1: 4.8 × 7.2 = 34.56 cm²
Area of Face 2: 3.4 × 7.2 = 24.48 cm²
Area of Face 3: 4.8 × 3.4 = 16.32 cm²

Adding the area of these 3 faces gives 75.36 cm², since each face is duplicated on the opposite side, the total surface area of the cuboid will be:
TSA = 2 (75.36) = 150.72 cm²
The length, width and height of a cuboid are 10cm, 8cm and 7cm respectively. Find the lateral surface area of a cuboid.

Math Solution:
Lateral surface area of cuboid is given by:
LSA = 2h(l+w)
Note :
l = length = 10 cm
w = width = 8 cm
h = height = 7 cm

Insert these values into the formula we will get:
LSA = 2 ×7(10 + 8)
LSA = 14 × 18
LSA = 252 cm2

The length, breadth and height of a cuboid are 16cm, 14cm and 10cm respectively. Find the total surface area of the cuboid.

Math Solution:
The total surface area of a cuboid is given by:
TSA = 2 (l*b + b*h + h*l)
Given that:
l = 16cm
b = 14cm
h = 10cm

Substituting the values in the equation we will get
TSA = 2 (16*4 + 14*10 + 10*16)
TSA = 2(224 + 140 + 160)
TSA = 2 * 524
TSA = 1048 cm2

Given a cereal box whose length is 20 cm, height is 30 cm and width is 8 cm. Find the surface area of the box.

Math Solution:
To find the surface are of the box we need to find the area of each rectangular face and add them all up.
The area of the front face is: 20 x 30 = 600 cm2.
The area of the top face is: 20 x 8 = 160 cm2.
The area of the side face is: 8 x 30 = 240 cm2.

Now add these values together we will get: 600 + 160 + 240 = 1000 cm2.

And the total surface area is therefore 1000 x 2 = 2000 cm2.

Find the surface area of a cuboid whose sides are 3cm by 6cm by 10cm.

Math Solution:
Surface area of the cuboid is given by:
TSA = 2 (16*4 + 14*10 + 10*16)
TSA = 2(3 x 6 + 6 x 10 + 3 x 10)
TSA = 2(18 + 60 + 30)
TSA = 216 cm2
That is smart math formula in aplication of Surface Area of a Cuboid. Formula Surface Area of a Cuboid Math

### Formula Math Of Cylinder

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.

Formula Math :
The area of each end cap can be found from the radius r of the circle, which is given by:
A = πr2

Thus the total area of the caps is 2πr2.

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 = 2πr2 + 2πrh

Smart Math Formula Note :
π  =  Pi, approximately 3.142,  r  = the radius of the cylinder, h  = height of the cylinder

By 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 × r2 + 2 × π × r × h
SA = 2 × 3.14 × 42 +  2 × 3.14 × 4 × 3
SA = 6.28 × 16 + 6.28 × 12
SA = 100.48 + 75.36
SA = 175.84
Surface Area = 175.84 cm2
•  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 cm2

•   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 cm2

•  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 cm2

• Find the radius of cylinder whose lateral surface area is 150 cm2 and its height is 9 cm.
Smart Solution:
Lateral surface area of cylinder is given by:
LSA = 2πrh
Given that:
LSA = 150cm2
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.