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There are two concentric circles whose areas are in the 9:16 and the difference between their diameters is 4cm. What is the area of the outer circle?
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There are two concentric circles whose areas are in the 9:16 and the d...
Problem:
There are two concentric circles whose areas are in the 9:16 and the difference between their diameters is 4cm. What is the area of the outer circle?
Solution:
Let the radii of the two concentric circles be r and R, where R>r.
Given that the ratio of their areas is 9:16, we have:
Area of inner circle / Area of outer circle = 9/16
Step 1:
Using the formula for the area of a circle, we can write:
πr² / πR² = 9/16
Step 2:
Simplifying this expression, we get:
r² / R² = 9/16
Step 3:
Taking the square root of both sides, we have:
r / R = 3/4
Step 4:
Since we know that the difference between their diameters is 4cm, we can write:
2R - 2r = 4
Step 5:
Simplifying this expression, we get:
R - r = 2
Step 6:
Solving the system of equations formed by steps 3 and 5, we get:
R = 8cm and r = 6cm
Step 7:
Finally, we can find the area of the outer circle using the formula for the area of a circle:
Area of outer circle = πR² = π(8)² = 64π square cm
Therefore, the area of the outer circle is 64π square cm.
There are two concentric circles whose areas are in the 9:16 and the difference between their diameters is 4cm. What is the area of the outer circle?
Solution:
Let the radii of the two concentric circles be r and R, where R>r.
Given that the ratio of their areas is 9:16, we have:
Area of inner circle / Area of outer circle = 9/16
Step 1:
Using the formula for the area of a circle, we can write:
πr² / πR² = 9/16
Step 2:
Simplifying this expression, we get:
r² / R² = 9/16
Step 3:
Taking the square root of both sides, we have:
r / R = 3/4
Step 4:
Since we know that the difference between their diameters is 4cm, we can write:
2R - 2r = 4
Step 5:
Simplifying this expression, we get:
R - r = 2
Step 6:
Solving the system of equations formed by steps 3 and 5, we get:
R = 8cm and r = 6cm
Step 7:
Finally, we can find the area of the outer circle using the formula for the area of a circle:
Area of outer circle = πR² = π(8)² = 64π square cm
Therefore, the area of the outer circle is 64π square cm.
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There are two concentric circles whose areas are in the 9:16 and the d...
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There are two concentric circles whose areas are in the 9:16 and the difference between their diameters is 4cm. What is the area of the outer circle?
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There are two concentric circles whose areas are in the 9:16 and the difference between their diameters is 4cm. What is the area of the outer circle? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about There are two concentric circles whose areas are in the 9:16 and the difference between their diameters is 4cm. What is the area of the outer circle? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two concentric circles whose areas are in the 9:16 and the difference between their diameters is 4cm. What is the area of the outer circle?.
There are two concentric circles whose areas are in the 9:16 and the difference between their diameters is 4cm. What is the area of the outer circle? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about There are two concentric circles whose areas are in the 9:16 and the difference between their diameters is 4cm. What is the area of the outer circle? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two concentric circles whose areas are in the 9:16 and the difference between their diameters is 4cm. What is the area of the outer circle?.
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