Chapter 11: Q. 81 (page 774)

Two circles have circumferences that add up to $12 π cm$ and areas that add up to $20 π {cm}^{2}$ . Find the radius of each circle.

Short Answer

Expert verified

The radius of the two circles are $2 a n d 4$ .

Step by step solution

Step 1. Given information.

Assume x to be the radius of the first circle and y to be the radius of the second circle.

From the question,

$2 πx + 2 πy = 12 π . . . . . . (i) {πx}^{2} + {πy}^{2} = 20 π . . . . . . (ii)$

Take out the common factors from equation (i),

$2 π (x + y) = 2 π (6) x + y = 6 . . . . . . . (iii)$

Take out the common factors from equation (ii),

$π (x^{2} + y^{2}) = 20 π x^{2} + y^{2} = 20 . . . . . . (iv)$

Step 2. Solve equation (iii) for x.

Solving equation (iii) for x,

$x = 6 - y$

Substitute the value of x in equation (iv),

localid="1646849857123" role="math" ${(6 - y)}^{2} + y^{2} = 20 (y - 4) (y - 2) = 0 y = 4, 2$

Substitute $y = 4$ in equation (iii),

$x + 4 = 6 x = 2$

Substitute $y = 2$ in equation (iii),

$x + 2 = 6 x = 4$

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Two circles have circumferences that add up to $12 π cm$ and areas that add up to $20 π {cm}^{2}$ . Find the radius of each circle.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve equation (iii) for x.

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Two circles have circumferences that add up to 12πcmand areas that add up to 20πcm2. Find the radius of each circle.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve equation (iii) for x.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Decision Maths

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Two circles have circumferences that add up to $12 π cm$ and areas that add up to $20 π {cm}^{2}$ . Find the radius of each circle.