To find the radius of the base of the cone formed from a sector of a circle, we need to follow a series of steps. Let's break it down step-by-step. ### Step 1: Understand the Problem We have a sector of a circle with: - Radius of the sector (circle) = 7.2 cm - Angle subtended at the center = 300° When this sector is rolled into a cone, the radius of the base of the cone will be determined by the arc length of the sector. ### Step 2: Calculate the Arc Length of the Sector The arc length (L) of a sector can be calculated using the formula: \[ L = \frac{\theta}{360^\circ} \times 2\pi r \] where: - \( \theta \) is the angle in degrees, - \( r \) is the radius of the sector. Substituting the values: - \( \theta = 300^\circ \) - \( r = 7.2 \, \text{cm} \) Calculating the arc length: \[ L = \frac{300}{360} \times 2\pi \times 7.2 \] \[ L = \frac{5}{6} \times 2\pi \times 7.2 \] \[ L = \frac{5 \times 2 \times 3.14 \times 7.2}{6} \] \[ L = \frac{5 \times 2 \times 3.14 \times 7.2}{6} \approx \frac{5 \times 45.216}{6} \approx \frac{226.08}{6} \approx 37.68 \, \text{cm} \] ### Step 3: Relate the Arc Length to the Cone's Base Radius When the sector is rolled into a cone, the arc length becomes the circumference (C) of the base of the cone. The circumference of a circle is given by: \[ C = 2\pi r_{cone} \] where \( r_{cone} \) is the radius of the base of the cone. Setting the arc length equal to the circumference: \[ L = C \implies 37.68 = 2\pi r_{cone} \] ### Step 4: Solve for the Radius of the Cone's Base Now, we can solve for \( r_{cone} \): \[ r_{cone} = \frac{L}{2\pi} = \frac{37.68}{2\pi} \] Using \( \pi \approx 3.14 \): \[ r_{cone} = \frac{37.68}{2 \times 3.14} \approx \frac{37.68}{6.28} \approx 6 \, \text{cm} \] ### Conclusion Thus, the radius of the base of the cone is **6 cm**. ### Why the Other Options are Incorrect - **Option A (8 cm)**: This is larger than the calculated radius and does not fit the relationship established by the arc length. - **Option C (9 cm)**: This is also larger than the calculated radius and similarly does not satisfy the arc length to circumference relationship. - **Option D (7 cm)**: This is still larger than the calculated radius and does not correspond to the arc length derived from the sector. ### Revision Summary - The arc length of the sector is calculated using the formula \( L = \frac{\theta}{360^\circ} \times 2\pi r \). - The arc length becomes the circumference of the cone's base when the sector is rolled into a cone. - The radius of the cone's base is found by rearranging the circumference formula \( C = 2\pi r_{cone} \). - The final answer for the radius of the base of the cone is **6 cm**.