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Hello students.
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Today we will discuss about this question.
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In this question we need to find the volume of the tetrahedron that is equal to question mark which is bounded by the coordinate plants and the plane that is x plus y plus z equals to three.
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And here we are given options we need to choose the correct option.
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So here first of all we are given that the plan equation that is x plus y plus y plus z is equal to 3 so that implies that x divide by 3 plus y divide by 3 plus z divide by 3 is equal to 1 now the volume of the tetrahedron v that is equal to triple integration d z divide d x so therefore as x plus y plus z is equal to 3 we can get z that is equals to 3 minus x minus y so z varies from 0 to 3 minus x minus y.
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Now y varies from 0 to 3 minus x and x varies from 0 to 3.
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So therefore volume v that is equals to 0 to 3 minus x 0 to 3 minus x 0 to 3 minus y d z, d y d x.
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So that is equals to integration 0 to 3, integration 0 to 3 minus x, z limit will be 0 to 3 minus x minus y, d, z.
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So that is equal to integration 0 to 3 to 3 minus x, 3 minus x, d, d, x, so that is equal to, v is equals to integration 0 to 3y minus xy minus y square divide by 2...