The volume of the outer layer is 2670.57 cubic centimeters.
Given
The aspherical object has a diameter of 18 cm.
It has a spherical inner core with a diameter of 9 cm.
<h3>The volume of outer layer;</h3>
The volume of the outer layer is given by the following formula;
![\rm Volume=\dfrac{4}{3}\pi r^3](https://tex.z-dn.net/?f=%5Crm%20Volume%3D%5Cdfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3)
The volume of the outer layer is given by;
Entire sphere - Inner sphere= Outer layer
Radius of Entire sphere = 9 cm
Radius of Inner sphere = 4.5 cm
Therefore,
The volume of the outer layer is;
![\rm Volume=\dfrac{4}{3}\pi [(Entire \ sphere)^3 - (Inner \ sphere)^3]\\\\Volume=\dfrac{4}{3}\pi (9^3-4.5^3)\\\\Volume=\dfrac{4}{3}\pi(729-91.12)\\\\Volume=\dfrac{4}{3}\times 3.14 \times 637.88\\\\ Volume = 2670.57](https://tex.z-dn.net/?f=%5Crm%20Volume%3D%5Cdfrac%7B4%7D%7B3%7D%5Cpi%20%5B%28Entire%20%5C%20sphere%29%5E3%20-%20%28Inner%20%5C%20sphere%29%5E3%5D%5C%5C%5C%5CVolume%3D%5Cdfrac%7B4%7D%7B3%7D%5Cpi%20%289%5E3-4.5%5E3%29%5C%5C%5C%5CVolume%3D%5Cdfrac%7B4%7D%7B3%7D%5Cpi%28729-91.12%29%5C%5C%5C%5CVolume%3D%5Cdfrac%7B4%7D%7B3%7D%5Ctimes%203.14%20%5Ctimes%20637.88%5C%5C%5C%5C%20Volume%20%3D%202670.57)
Hence, the volume of the outer layer is 2670.57 cubic centimeters.
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