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Answer:

Volume of hemisphere =

[tex] \frac{2}{3} \pi \: r {}^{3} [/tex]

Given volume =

[tex]18\pi \: cube[/tex]

[tex] \frac{2}{3} \times \frac{22}{7} \: {r}^{3} = 18 \times \frac{22}{7} [/tex]

So pi is there on both the sides so it will be cut from both LHS and RHS

[tex] \frac{2}{3} \times r {}^{3} = 18[/tex]

[tex]2 \times r {}^{3 } = 18 \times 3[/tex]

[tex]2 \times r {}^{3} = 54[/tex]

[tex]r {}^{3} = \frac{54}{2} [/tex]

[tex]r {}^{3} = 27[/tex]

[tex]r = 3[/tex]

Therefore value of r=3 inches

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