IB Mathematics Analysis and Approaches Question Type 4: Applying Both Arc Length and Area of Sector in Solving Equations Exercises

A sector has area $12\pi$ and subtends an arc of length $6\pi$. Determine the radius of the circle and the measure of the central angle in degrees.

A quarter circle has an arc length of $8\pi$. Find the radius of the circle and the area of the quarter circle.

A sector's arc length is one quarter of the circle's circumference and its area is $9\pi$. Find the circle's radius.

A sector has area $18\pi$ and central angle $\frac{3\pi }{4}$ radians. Find the radius of the circle.

Find the radius and the common numerical value.

A sector has arc length $9$ and area $18$. Find the radius of the circle and the central angle in radians.

A sector with central angle $\frac{2\pi }{3}$ radians has an arc length of $10\pi$. Find the radius of the circle and the area of the sector.

A sector has central angle $150^{\circ }$ and an arc length of $5\pi$ cm. Find its radius and area.

A sector with central angle $\frac{\pi }{3}$ has its area equal to three times its arc length. Find the radius of the circle.

A full circle is partitioned into a sector that has one-sixth of the circumference as its arc and an area of $20\pi$. Find the circle's radius.

A sector has area $8\pi$ and arc length $4\pi$. Find the radius of the circle and the measure of its central angle in radians.

A sector has an arc length of $15$ and an area of $30$. Find the radius of the circle and the measure of the central angle in radians.