Question

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 1

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=$\pi r$ 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
                                                        = $\pi r$+$2r$
                                                       $\ne$ 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.