Question

The area of a semicircle of diameter ‘d’ is ______.

विकल्प

• `(πd^2)/16`

• `(πd^2)/4`

• `(πd^2)/8`

• `(πd^2)/2`

Answer 1

The area of a semicircle of diameter ‘d’ is `underlinebb((πd^2)/8)`.

Explanation:

1. Identify the area of a circle

The area `A_"circle"` of a complete circle in terms of its radius r is given by the formula:

`A_"circle" = πr^2`

2. Express area using diameter

The diameter d is twice the radius (d = 2r), which means `r = d/2`.

Substituting this into the circle area formula:

`A_"circle" = π(d/2)^2`

= `π(d^2/4)`

= `(πd^2)/4`

3. Calculate the semicircle area

A semicircle is exactly half of a full circle.

Therefore, its area `A_"semicircle"` is:

`A_"semicircle" = 1/2 xx A_"circle"`

`A_"semicircle" = 1/2 xx (πd^2)/4`

`A_"semicircle" = (πd^2)/8`