Question

The sum of the areas of two circles is 80 square meters.find the length of a radius of each circle is one of them is twice as long as the other

Answer 1

Correct Question:

The sum of the areas of two circles is 80π metre sqr. find the length of a radius of each circle is one of them is twice as long as the other.

Answer:

$\large \boxed{\boxed{\mathtt{4m \: and \: 8m}}}$

Step-by-step Explanation:

Given :

• The sum of the areas of two circles is 80 square meters.

• And radius of one circle is twice the other circle.

To find :

• Length of radius of each circle .

Solution :

According to question

It's given that radius of one circle is twice the other .

Therefore let,

$\implies \textsf{Radius of smaller circle = r}$

and thus

$\implies \textsf{Radius of larger circle = 2r}$

Now we know that,

$\boxed{ \mathtt{\bigstar \; Area \: of \: Circle = \pi r^2}}$

Therefore,

$\longrightarrow \mathsf{Area \: of \: Smaller \: Circle ({C}_{1}) = \pi {(r)}^{2}}$

and

$\longrightarrow \mathsf{Area \: of \: larger \: Circle\: ({C}_{2}) = \pi {(2r)}^{2}}$

$\longrightarrow \mathsf{Area \: of \: larger \: Circle ({C}_{2}) = \pi 4{r}^{2}}$

Now according to question

$\longrightarrow \: \mathsf{{C}_{1} + {C}_{2} = 80 \pi m^2}$

$\longrightarrow \: \mathsf{ \pi r^2 + \pi 4{r}^{2}= 80 \pi m^2}$

$\longrightarrow \: \mathsf{ \pi r^2(1 + 4) = 80 \pi m^2}$

$\longrightarrow \: \mathsf{ \pi r^2(5) = 80 \pi m^2}$

$\longrightarrow \: \mathsf{ \pi r^2 = \dfrac{80 \pi m^2}{5}}$

$\longrightarrow \: \mathsf{ \pi r^2 = 16 \pi m^2}$

$\longrightarrow \: \mathsf{ r^2 = 16m^2}$

$\longrightarrow \: \mathsf{ r = \sqrt{16m^2}}$

$\longrightarrow \: \mathsf{ r = 4m}$

Therefore we have

$\implies \textsf{Radius of smaller circle = r = 4m}$

$\implies \textsf{Radius of smaller circle = 2r = 2(4m) = 8m }$

Thus Required answer =

$\large \underline{\boxed{\mathtt{4m \: and \: 8m}}}$

Answer 2

Given :-----

• Sum of Areas of 2 circles = 80m²
• Radius of one circle = 2 × radius of another circle

To Find :-------

• R1 = Radius of Bigger circle (Let)
• R2 = Radius of smaller circle (Let)

Formula used :---

• Area of Circle = πr²

Solution :------

Area of bigger circle = πr² = π(R1)²

since , R1 = 2R2

→ Area of bigger circle = π(2R2)² = 4π(R2)² -----------Equation(1)

Area of smaller circle = πr² = π(R2)² ----------- Equation(2)

Adding both Equation Now, we get, sum of areas of two circles that is given = 80m²

so,

$4\pi \: (R2)^{2} + \pi {(R2)}^{2} = 80 \\ \\ \implies \: 5\pi(R2)^{2} = 80 \\ \\ \implies \: (R2)^{2} \: = \frac{80 \times 7}{5 \times 22} \\ \\ \implies \: (R2)^{2} \: = 5.09 \\ \\ \implies \: (R2) = \sqrt{5.09} = 2.25$

so, Radius of smaller circle = 2.25 m Approx)

Radius of larger circle = 2.25×2 = 5m (Approx)

(Hope it helps you)