
Draw a semi-circle with centre O and radius 5cm. Is the diameter that determines the semi-circle, a part of the semi-circle?
Answer
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Hint: In this question first we need to make a figure of semi-circle then using the definition of semi-circle we check if the diameter that determines the semi-circle, a part of the semi-circle or not. We can also check this using the formula of circumference of semicircle.
Complete step-by-step solution -
Above figure is of a semi-circle with centre O and radius 5cm.
The endpoints of a diameter of a circle divides it into two equal parts, and each part is called a semi-circle.
So, it is not the diameter, but the end points of the diameter that determines the semi-circle or a part of the semi-circle.
We can understand it using circumference formula of semi-circle,
Circumference of semi-circle= eq.1
And the circumference of semicircle with diameter that determines it = circumference of semicircle
+ diameter of circle of which semi-circle is a part
= +
circumference of circle
Hence, the diameter that determines the semi-circle, is not the part of the semi-circle.
Note: Whenever you get this type of question the key concept to solve this is to have knowledge about semi-circle and its formulas of area and circumference. One more thing to be remembered is that circumference of a circle is defined as the linear distance around it. In other words, if a circle is opened to form a straight line then the length of that line will be the circumference of the circle.
Complete step-by-step solution -

Above figure is of a semi-circle with centre O and radius 5cm.
The endpoints of a diameter of a circle divides it into two equal parts, and each part is called a semi-circle.
So, it is not the diameter, but the end points of the diameter that determines the semi-circle or a part of the semi-circle.
We can understand it using circumference formula of semi-circle,
Circumference of semi-circle=
And the circumference of semicircle with diameter that determines it = circumference of semicircle
+ diameter of circle of which semi-circle is a part
=
Hence, the diameter that determines the semi-circle, is not the part of the semi-circle.
Note: Whenever you get this type of question the key concept to solve this is to have knowledge about semi-circle and its formulas of area and circumference. One more thing to be remembered is that circumference of a circle is defined as the linear distance around it. In other words, if a circle is opened to form a straight line then the length of that line will be the circumference of the circle.
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