Question

A circle has a diameter of 7
inches. What is the area of
the circle in terms of pi?

Answer 1

Circle:

A Circle is a closed plane geometric shape figure. The diameter of a circle is the longest chord of a circle. The radius drawn perpendicular to the chord bisects the chord. A Circle is always lie at an equal distance from a center point. Circles having different radius are similar.

Area of Circle:

The area of a circle is pi times the radius squared. The unit of area of circle is square units.

`\longrightarrow Area_((circle)) = \pi r^2`

Here, r is the radius of the circle.

Elucidation:

We are asked to find the area of the circle in terms of pi if the diameter is 7 inches.

We know that, the diameter is twice the length of the radius of a circle. Therefore;

• D = 2r
• r = D/2 = 7/2 = 3.5

Now the area of circle will be:

`\implies Area_((circle)) = \pi r^2`

`\implies Area_((circle)) = \pi (3.5)^2`

`\implies Area_((circle)) = 12.25 \pi`

Hence, the area of the given circle is 12.25π square inches.

Answer 2

• Area of circle = 12.25π square inches

Explanation:

In the question we are given that diameter of circle is of 7 inches . And we have asked to find the area of the circle in term of pi ( π ) .

For finding area of circle we must have to know that what is the formula for finding area of circle. So :

`\qquad \qquad \: \red{\underline{\red{ \boxed{ \frak{Area \: of \: Circle = \pi r {}^(2) }}}}}`

Where ,

• π refers to 3.14 or 22/7

• r refers to radius of circle

Solution : -

As in the question we are given length of diameter . So for finding area we need to find the radius of circle .

We know that diameter of circle is two times its radius or ,

`\qquad \: \rm {Diameter = 2 × Radius }`

So for radius we are dividing both side with 2 :

`\qquad \: \rm { (Diameter)/(2) = \frac{ \cancel{2} × Radius}{ \cancel{2}} }`

We get that ,

`\qquad \: \rm {Radius = (Diameter)/(2) }`

Therefore , we can say that radius of circle is half of its diameter .

Now using this firstly we are finding radius of circle . So :

`\longmapsto \quad \: \boxed{\rm{ Radius = (7)/(2) \: \: inches}}`

• Therefore , radius of circle is 7/2 inches .

Now , we are moving towards our final solution .

So ,

`\longrightarrow \quad \: Area_ { (Circle)} = \pi( (7)/(2) ) {}^(2)`

Calculating further :

`\longrightarrow \quad \: Area_ { (Circle)} = \pi * (7)/(2) * (7)/(2)`

After multiplication of 7/2 with 7/2 we get :

`\longrightarrow \quad \: Area_ { (Circle)} = \pi * (49)/(4)`

On dividing 49 by 4 we get :

`\longrightarrow \quad \: \blue{{\boxed{\frak{Area_ { (Circle)} = 12.25\pi \: inches {}^(2) }}}}`

Remember one thing , we haven't put value of π as 22/7 or 3.14 because in the question it is given that we have to find the area of circle in terms of pi .

• Henceforth , in terms of pi ( π ) area of circle having diameter 7 inches is 12.25π inches² .

#Keep Learning