# 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.

Last updated date: 20th Mar 2023

•

Total views: 303.9k

•

Views today: 6.82k

Answer

Verified

303.9k+ 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.

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

Paulings electronegativity values for elements are class 11 chemistry CBSE

For a particle executing simple harmonic motion the class 11 physics CBSE

Does Nichrome have high resistance class 12 physics CBSE

The function f satisfies the functional equation 3fleft class 12 maths JEE_Main

Write a letter to the Principal of your school to plead class 10 english CBSE

Look at the handout below Write a letter to the organizers class 11 english CBSE

Trending doubts

What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?