Part B Layers of wool are wound tightly around each core, resulting in a sphere with a radius of approximately 1.41 inches. What is the volume of the wool without the core? Round to the nearest hundredth.

To find the volume of the wool without the core, we need to subtract the volume of the core from the total volume of the sphere. Given: - Radius of the sphere (including the core) = 1.41 inches The volume of a sphere is given by the formula: \[ V = \frac{4}{3} \pi r^3 \] Where: - \( V \) is the volume of the sphere - \( r \) is the radius of the sphere First, let's calculate the volume of the sphere including the core: \[ V_{\text{total}} = \frac{4}{3} \pi (1.41)^3 \] Next, we need to find the volume of the core. Since the core is a sphere, we can use the same formula: \[ V_{\text{core}} = \frac{4}{3} \pi r_{\text{core}}^3 \] However, we are not given the radius of the core. Since the wool is wound tightly around the core, we can assume that the radius of the core is negligible compared to the radius of the sphere. Therefore, we can approximate the volume of the core as zero. Now, we can calculate the volume of the wool without the core by subtracting the volume of the core from the total volume of the sphere: \[ V_{\text{wool}} = V_{\text{total}} - V_{\text{core}} \] Let's calculate the volume of the wool without the core. Simplify the expression by following steps: - step0: Solution: \(\frac{4}{3}pi\times 1.41^{3}\) - step1: Convert the expressions: \(\frac{4}{3}pi\left(\frac{141}{100}\right)^{3}\) - step2: Multiply the numbers: \(\frac{4}{3}ip\left(\frac{141}{100}\right)^{3}\) - step3: Multiply the numbers: \(\frac{9\times 47^{3}}{250000}ip\) The volume of the wool without the core is approximately 11.74 cubic inches. Rounding to the nearest hundredth, the volume of the wool without the core is approximately 11.74 cubic inches.