Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm.
33 cm
Step 1: Recall the formula for the circumference of a circle:
\(C = 2 \pi r\), where \(r\) is the radius.
Step 2: Write the circumference of each given circle:
Step 3: Add the two circumferences:
\(C_1 + C_2 = 30\pi + 36\pi = 66\pi\,\text{cm}\).
Step 4: Let the required radius be \(R\). Its circumference is:
\(C = 2 \pi R\).
Step 5: According to the question:
\(2 \pi R = 66\pi\).
Step 6: Cancel \(\pi\) on both sides:
\(2R = 66\).
Step 7: Divide both sides by 2:
\(R = 33\,\text{cm}\).
Final Answer: The radius of the required circle is 33 cm.