Answer:
The volume of the outer layer is 2670.57 cm³ .
Step-by-step explanation:
Formula
\(Volume\ of\ a\ sphere = \frac{4}{3} \pi r^{3}\)
Where r is the radius of the sphere .
As given
A spherical object has a diameter of 18 cm.
It has a spherical inner core with a diameter of 9 cm.
Let us assume that the radius of the spherical object is represented by R .
Let us assume that the radius of the inner object is represented by r .
\(Diameter (R) = \frac{18}{2}\)
= 9 cm
\(Diameter (R) = \frac{9}{2}\)
= 4.5 cm
\(\pi = 3.14\)
Volume of the outer layer = Volume of the spherical object - Volume of the inner core .
\(Volume\ of\ a\ outer\ layer = \frac{4}{3}\times 3.14\times 9\times 9\times 9 - \frac{4}{3}\times 3.14\times 4.5\times 4.5\times 4.5\)
\(Volume\ of\ a\ outer\ layer = \frac{4\times 3.14\times 9\times 9\times 9}{3}- \frac{4\times 3.14\times 4.5\times 4.5\times 4.5}{3}\)
\(Volume\ of\ a\ outer\ layer = \frac{9156.24}{3}- \frac{1144.53}{3}\)
\(Volume\ of\ a\ outer\ layer = 3052.08-381.51\)
\(Volume\ of\ a\ outer\ layer = 2670.57\ cm^{3}\)
Therefore the volume of the outer layer is 2670.57 cm³ .
