Area Of A Semi Cylinder
In geometry, a semicircle is a plane figure that is formed by dividing a circle into exactly two parts. So, nosotros can write the formulas of area and perimeter for a semicircle using the area and perimeter of a circle. In this article, you volition learn how to identify a semicircle and find the surface area and perimeter of a semicircle with the assist of formulas and solved examples.
What is a Semi-Circle?
A semicircle is formed when a lining passing through the centre touches the two ends on the circle. Thus, by joining two semicircles we get a round shape.
Semi Circle Shape
When a circle is cutting into two halves or when the circumference of a circle is divided by 2, we go a semicircular shape.
Since a semicircle is one-half that of a circumvolve, hence the surface area volition be half that of a circle.
In the beneath figure, the line AC is called the bore of the circumvolve. The diameter divides the circle into two halves such that they are equal in area. These two halves are referred to every bit the semicircles.
A circumvolve is a locus of points equidistant from a given point which is the eye of the circumvolve. The common distance from the eye of a circle to its point is called a radius.
Thus, the circumvolve is entirely defined by its eye (O) and radius (r).
Area of Semi-Circumvolve
The area of a semicircle is half of the surface area of the circle. As the area of a circle is πr2. So, the area of a semicircle is 1/two(πr2 ), where r is the radius. The value of π is iii.14 or 22/7.
Area of Semicircle = one/2 (π r2)
Derivation
As defined above, the area of a semicircle is half of the area of a circle. Also, we tin can say that the area of a circle is the number of square units inside that circumvolve.
Allow us generate the above figure. This polygon can be broken into n isosceles triangle (equal sides being radius).
Thus, one such isosceles triangle can be represented as shown below.
The area of this triangle is given equally ½(h*s)
Now for n number of polygons, the surface area of a polygon is given as
½(n*h*s)
The term north × s is equal to the perimeter of the polygon. Every bit the polygon gets to expect more and more like a circle, the value approaches the circle circumference, which is 2 × π × r. So, substituting 2×π×r for n × s.
Polygon area = h/2(2 × π × r)
Likewise, every bit the number of sides increases, the triangle gets narrower then when south approaches goose egg, h and r have the aforementioned length. And then substituting r for h:
Polygon surface area = h/two(2 × π × r)
= (two × r × r × π)/2
Rearranging this we go
Surface area = πr2
At present the area of a semicircle is equal to half of that of a full circle.
Therefore,
Expanse of a semicircle = (πr2)/two
Perimeter of Semicircle
The perimeter of a semicircle is the sum of one-half of the circumference of the circle and its diameter. Every bit the perimeter of a circle is 2πr or πd. So, the perimeter of a semicircle is 1/two (πd) + d orπr + 2r, where r is the radius.
Therefore,
Or
Circumference = (πr + 2r)
Semi circle Formula
The below tabular array shows the formulas associated with the semicircle of radius r.
| Surface area | (πr2)/2 |
| Perimeter (Circumference) | (½)πd + d; when diameter (d) is known |
| πr + 2r | |
| Angle in a semicircle | 90 degrees, i.e. right angle |
| Central bending | 180 degrees |
Video Lessons on Circles
Introduction to Circles
Parts of a Circle
Area of a Circumvolve
All almost Circles
Semi circumvolve Examples
Example 1:
Find the area of a semicircle of radius 28 cm.
Solution:
Given,
Radius of semi circle = r = 28 cm
Area of semi circumvolve = (πr2)/two
= (½) × (22/vii) × 28 × 28
= 1232
Therefore, the expanse of the semi-circle is 1232 sq. cm.
Example 2:
What is the perimeter of a semicircle with a diameter of seven cm?
Solution:
Given,
Diameter of semicircle = d = 7 cm
Formula for the circumference (perimeter) of a semicircle using its bore = (½)πd + d
Substitute the value of d, nosotros get;
= (½) × (22/7) × 7 + 7
= 11 + vii
= xviii
Therefore, the perimeter of the semicircle is eighteen cm.
Do Problems
- Observe the circumference and area of a semicircle whose bore is 21 cm.
- If the perimeter of a semicircle is 36 units, then notice the radius.
- Is the perimeter of a semicircle half the perimeter of a circumvolve? Justify your answer.
Frequently Asked Questions on Semicircle
Is a semicircle one-half the circle?
Yes, a semicircle is half the circumvolve. That means a circle can be divided into 2 semicircles.
What shape is a semicircle?
The shape of a semicircle will exist obtained past cutting a circle along its diameter and the full arc of a semicircle e'er measures 180 degrees. An example of a semicircular shape is a protractor.
What is the semicircle angle?
The angle made by the triangle in a semicircle is a right angle, i.e. xc degrees.
What is the area of a semicircle?
The area of a semicircle with radius r is equal to half the area of the circle.
Area of semicircle = (1/2) × Area of circumvolve = (i/2)πr^two
What is the perimeter formula of a semicircle?
The perimeter formula of the semicircle of radius r is given past:
Semicircle circumference = (one/2)2πr + 2π = πr + 2r
Area Of A Semi Cylinder,
Source: https://byjus.com/maths/semi-circle/
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