Mathematics: The internal and external diameters of a spherical shell are 12cm and 18cm calculate the volume

Step-by-step explanation:We first rationalize the denominator. This means we multiply the numerator and denominator by a factor that will make the denominator a whole number.Our denominator is ; this can also be written as .For 9 to be a whole number, its exponent must be a whole number. We want to add 2/3 to the exponent of 9 on the bottom; this means we multiply by :On the numerator, this gives us:6(9^(2/3))-3(6^(1/3))(9^(2/3))= On the denominator, we will have:(9^(1/3))(9^(2/3)) = 9^(3/3) =...

The internal and external diameters of a spherical

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Jadethepartyanimal

10.04.2023

Mathematics

$2\sqrt[3]{3}-\sqrt[3]{18}$

Step-by-step explanation:

We first rationalize the denominator. This means we multiply the numerator and denominator by a factor that will make the denominator a whole number.

Our denominator is $\sqrt[3]{9}$ ; this can also be written as $9^{\frac{1}{3}}$ .

For 9 to be a whole number, its exponent must be a whole number. We want to add 2/3 to the exponent of 9 on the bottom; this means we multiply by $9^{\frac{2}{3}}$ :

On the numerator, this gives us:

6(9^(2/3))-3(6^(1/3))(9^(2/3))

= $6\sqrt[3]{9(9)} -3\sqrt[3]{2(3)}(\sqrt[3]{9(9)}) \\\\=6\sqrt[3]{3(3)(3)(3)}-3\sqrt[3]{2(3)(3)(3)(3)(3)}\\\\=6(3)\sqrt[3]{3}-3(3)\sqrt[3]{2(3)(3)}\\\\=18\sqrt[3]{3}-9\sqrt[3]{18}$

On the denominator, we will have:

(9^(1/3))(9^(2/3)) = 9^(3/3) = 9^1 = 9

This gives us:

$\frac{18\sqrt[3]{3}-9\sqrt[3]{18}}{9}\\\\=2\sqrt[3]{3}-\sqrt[3]{18}$

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The internal and external diameters of a spherical shell are 12cm and 18cm calculate the volume

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