Question

What is the diameterof the circle if its area is 5000 cm^2?
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Answer 1

GIVEN :–

• Area of circle = 5000 cm².

TO FIND :–

• Diameter of circle = ?

• SOLUTION :–

• If radius of circle is 'r' , then area of circle is –

$\\ \bigstar \: \: \:\: \large { \boxed{ \bold{A = \pi {r}^{2} }}}$

• Now put the values –

$\\ \implies { \bold{5000 = \pi {r}^{2} }}$

$\\ \implies { \bold{5000 = \dfrac{22}{7} {r}^{2} }}$

$\\ \implies { \bold{5000 \left(\dfrac{7}{22} \right) = {r}^{2} }}$

$\\ \implies { \bold{ {r}^{2} = \left(\dfrac{35000}{22} \right) }}$

$\\ \implies { \bold{ {r}^{2} = 1590.9}}$

$\\ \implies { \bold{r = \sqrt{1590.9}}}$

$\\ \implies \large { \boxed { \bold{r = 39.89 \: cm}}}$

• We know that –

$\\ \implies { \bold{Diameter = 2(radius)}}$

$\\ \implies { \bold{Diameter = 2(39.89)}}$

$\\ \implies \large { \boxed { \bold{Diameter = 79.78 \: cm}}}$

Answer 2

Here,

Area = 3000cm^2

Diameter = ?

Now,

Radius = πr^2

=39.8

Diameter = 2r

=79.8