The volume of the right pyramid is 864 cm³.
The given parameters;
The volume of a right pyramid is one-third the product of the base and the perpendicular height.
The diagonal length of the right pyramid is calculated as follows;
[tex]d^2 = b^2 + b^2\\\\ d^2 = (\sqrt{288})^2 + (\sqrt{288} )^2 \\\\ d ^2 = 576\\\\ d = \sqrt{576} \\\\ d = 24 \ cm[/tex]
The perpendicular height of the right pyramid is calculated as follows;
[tex](\frac{d}{2} )^2 + h^2 = 15^2\\\\ (\frac{24}{2})^2 + h^2 = 15^2\\\\ 144 + h^2 = 225\\\\ h^2 = 225-144\\\\ h^2 = 81\\\\ h = \sqrt{81} \\\\ h = 9 \ cm[/tex]
The volume of the right pyramid is calculated as follows;
[tex]V = \frac{1}{3} \times b \times h\\\\ V = \frac{1}{3} \times 288 \times 9\\\\ V = 864 \ cm^3[/tex]
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