Question

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Answer 1

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 .

Answer 2

The answer is 2670.57 (i just took the quiz so this is the answer for sure)