Question

the sum of the area of two circles 770cm²and radius of one of them is 14cm.find the radius of other circle?​

Answer 1

Answer:

Radius of the other circle = 7 cm

Step-by-step explanation:

Given :

Sum of the area of the two circles = 770 cm²

Radius of one of the circle = 14 cm

To find :

The radius of other circle

Taken :

So , the formula to find the area of the circle -:

$\boxed{\sf{A=\pi{r}^{2}}}$

Where,

A = Area

r = Radius

Let the radius of other circle be x

So , now to find the radius of the other circle use this formula -:

$\boxed{\sf{A=\pi{r}^{2}+\pi{r}^{2}}}$

Solution :

$:\implies\sf{{770cm}^{2}=\dfrac{22}{7}\times{14cm}^{2}+\dfrac{22}{7}\times{x}^{2}}$

$:\implies\sf{{770cm}^{2}=\dfrac{22}{7}\times(14\times14)+\dfrac{22}{7}\times{x}^{2}}$

$:\implies\sf{{770cm}^{2}=\dfrac{22}{\cancel{7}}\times\cancel{196cm}+\dfrac{22}{7}\times{x}^{2}}$

$:\implies\sf{{770cm}^{2}=22\times28+\dfrac{22}{7}\times{x}^{2}}$

$:\implies\sf{{770cm}^{2}={616cm}^{2}+\dfrac{22}{7}\times{x}^{2}}$

$:\implies\sf{{770cm}^{2}-{616cm}^{2}=\dfrac{22}{7}\times{x}^{2}}$

$:\implies\sf{{154cm}^{2}=\dfrac{22}{7}\times{x}^{2}}$

$:\implies\sf{\cancel{\dfrac{{154cm}^{2}\times7}{22}}={x}^{2}}$

$:\implies\sf{\sqrt{49cm}=x}$

$:\implies\sf{7cm=x}$

So , the radius of the other circle is 7 cm .

Answer 2

Question :-

• the sum of the area of two circles 770cm²and radius of one of them is 14cm.find the radius of other circle?

Given :-

• Area of 2 circles = 770cm²
• Radius of 1 circle = 14cm

To Find :-

• What is the Radius of the second circle ?

Solution :-

$\bigstar \: \underline{ \: {\bf{Area \:of \: 2 \: Circle\: =\pi{r}^{2}+\pi{r}^{2}}}} \: \: \bigstar$

$\longmapsto\sf{{770cm}^{2}=\dfrac{22}{7}\times{14cm}^{2}+\dfrac{22}{7}\times{x}^{2}}$

$\longmapsto\sf{{770cm}^{2}=\dfrac{22}{7}\times(14\times14)+\dfrac{22}{7}\times{x}^{2}}$

$\longmapsto\sf{{770cm}^{2}=\dfrac{22}{\cancel{7}}\times\cancel{196cm}+\dfrac{22}{7}\times{x}^{2}}$

$\longmapsto\sf{{770cm}^{2}=22\times28+\dfrac{22}{7}\times{x}^{2}}$

$\longmapsto\sf{{770cm}^{2}={616cm}^{2}+\dfrac{22}{7}\times{x}^{2}}$

$\longmapsto\sf{{770cm}^{2}-{616cm}^{2}=\dfrac{22}{7}\times{x}^{2}}$

$\longmapsto\sf{{154cm}^{2}=\dfrac{22}{7}\times{x}^{2}}$

$\longmapsto\sf{\dfrac{{154}\times7}{22}={x}^{2}}$

$\longmapsto\sf{\cancel{\dfrac{{1078}}{22}}={x}^{2}}$

$\longmapsto\sf { 49={x}^{2}}$

$\longmapsto\sf{\sqrt{49cm}=x}$

$\longmapsto{\boxed{\bf{7cm=x}}}$

━━━━━━━━━━━━

$\therefore$ The radius of the other circle is 7 cm .

━━━━━━━━━━━━

Formulas Related to Area :-

• Area of Square = Side x Side
• Area of Rectangle = Length × Breadth
• Area of Triangle = ½ × base x height
• Area of parallelogram = base x height
• Area of circle = πr²
• Area of Rhombus = ½ × product of its diagonals
• Area of Trapezium = ½ × height × sum of parallel sides
• Area of Polygon = sum of the area of all regions into which it is divided

━━━━━━━━━━━━