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

Answer:

• Area of circle = 12.25π square inches

Step-by-step 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 :

$\qquad \: \rm { \dfrac{Diameter}{2} = \dfrac{ \cancel{2} × Radius}{ \cancel{2}} }$

We get that ,

$\qquad \: \rm {Radius = \dfrac{Diameter}{2} }$

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

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

$\longmapsto \quad \: \boxed{\rm{ Radius = \frac{7}{2} \: \: inches}}$

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

Now , we are moving towards our final solution .

So ,

$\longrightarrow \quad \: Area_ { (Circle)} = \pi( \dfrac{7}{2} ) {}^{2}$

Calculating further :

$\longrightarrow \quad \: Area_ { (Circle)} = \pi \times \dfrac{7}{2} \times \dfrac{7}{2}$

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

$\longrightarrow \quad \: Area_ { (Circle)} = \pi \times \dfrac{49}{4}$

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 .

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