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  • Find the volume V of the described solid S. The base of S is an elliptical region with boundary curve 9x^2 + 16y^2 = 144. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.

Find the volume V of the described solid S. The base of S is an elliptical region with boundary curve 9x^2 + 16y^2 = 144. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.

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Because;the;cross;sections;are;isosceles;right;triangles;with\* hypotenuse;in;the;base,;the;length;of;the;hypotenuse;is;6sqrt1-fracx^24,\*which;means;that;the;area;of;the;cross;section;is; 9(1-fracx^24)\*Rightarrow int_-2^29(1-fracx^24);dx\* Rightarrow 9x-frac9x^312= 9(2)-frac3 imes (2)^34-9(-2)+ frac3 imes (-2)^34\*Rightarrow 18-6+18-6=24\* herefore required; area;will;be;24;sq.;units

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Deependra Verma

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