Answer
450.9k+ views
Hint: Assume a variable r that will represent the radius of the circle whose circumference is equal to the sum of the circumference of the circles having radius 19 cm and 9 cm. For a circle with radius equal to r, the circumference is given by the formula $2\pi r$. Using this formula, the question can be solved.
Complete step-by-step answer:
Before proceeding with the question, we must know all the formulas that will be required to solve this question.
Consider a circle having its radius equal to r. To find the circumference of this circle, we use the formula,
C = $2\pi r$ . . . . . . . . . . . (1)
In the question, we have to find the radius of the circle whose circumference is equal to the sum of the circumference of the circles having radius 19 cm and 9 cm.
Let us assume the radius of this circle as r. Using formula (1), the circumference of this circle is,
C = $2\pi r$ . . . . . . . . (2)
Using formula (1), the circumference of the circle with radius 19 cm is equal to,
${{C}_{1}}=2\pi \left( 19 \right)$ . . . . . . . . (3)
Using formula (1), the circumference of the circle with radius 9 cm is equal to,
${{C}_{2}}=2\pi \left( 9 \right)$ . . . . . . . . (4)
In the question, it is given that,
$C={{C}_{1}}+{{C}_{2}}$
Substituting C from equation (2), ${{C}_{1}}$ from equation (3) and ${{C}_{2}}$ from equation (4) in the above equation, we get,
$\begin{align}
& 2\pi r=2\pi \left( 19 \right)+2\pi \left( 9 \right) \\
& \Rightarrow 2\pi r=2\pi \left( 19+9 \right) \\
& \Rightarrow 2\pi r=2\pi \left( 28 \right) \\
& \Rightarrow r=28cm \\
\end{align}$
Hence, the answer is 28 cm.
Note: This question can be done directly if one knows that the circumference is linearly proportional to the radius of the circle. Since the circumference of the first circle is equal to the sum of the circumference of the other two circles, we can say that the radius of the first circle is equal to the sum of the radius of the other two circles.
Complete step-by-step answer:
Before proceeding with the question, we must know all the formulas that will be required to solve this question.
Consider a circle having its radius equal to r. To find the circumference of this circle, we use the formula,
C = $2\pi r$ . . . . . . . . . . . (1)
In the question, we have to find the radius of the circle whose circumference is equal to the sum of the circumference of the circles having radius 19 cm and 9 cm.
Let us assume the radius of this circle as r. Using formula (1), the circumference of this circle is,
C = $2\pi r$ . . . . . . . . (2)
Using formula (1), the circumference of the circle with radius 19 cm is equal to,
${{C}_{1}}=2\pi \left( 19 \right)$ . . . . . . . . (3)
Using formula (1), the circumference of the circle with radius 9 cm is equal to,
${{C}_{2}}=2\pi \left( 9 \right)$ . . . . . . . . (4)
In the question, it is given that,
$C={{C}_{1}}+{{C}_{2}}$
Substituting C from equation (2), ${{C}_{1}}$ from equation (3) and ${{C}_{2}}$ from equation (4) in the above equation, we get,
$\begin{align}
& 2\pi r=2\pi \left( 19 \right)+2\pi \left( 9 \right) \\
& \Rightarrow 2\pi r=2\pi \left( 19+9 \right) \\
& \Rightarrow 2\pi r=2\pi \left( 28 \right) \\
& \Rightarrow r=28cm \\
\end{align}$
Hence, the answer is 28 cm.
Note: This question can be done directly if one knows that the circumference is linearly proportional to the radius of the circle. Since the circumference of the first circle is equal to the sum of the circumference of the other two circles, we can say that the radius of the first circle is equal to the sum of the radius of the other two circles.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)