The volume of the tetrahedron bounded by the planeand the co-ordinate planes isequal toa)1/3πabcb)2/3πabcc)1/6πabcd)None of theseCorrect answer is option 'D'. Can you explain this answer?

Question

The volume of the tetrahedron bounded by the planeand the co-ordinate planes isequal toa)1/3&pi;abcb)2/3&pi;abcc)1/6&pi;abcd)None of theseCorrect answer is option 'D'. Can you explain this answer?

Answer

Here
Let u = x/a, v = y/b , w = z/c
Then dx = a du, dy = b dv, dz = c dw
So, Required volume
V =

abc du dv dw
where u + v + w ≤ 1, u ,v ,w ≥ 0
Thus

Hence, the correct answer is (d)

Similar Mathematics Doubts

The volume of the tetrahedron bounded by the planeand the co-ordinate planes isequal to

Volume of the solid generated by revolving the region bounded by the lines x = 0 , x = 2 and the curve about the line y = 2 is equal to _______. Correct answer is '6.345'. Can you explain this answer?

The volume of the solid bounded by the paraboloid z = x2 + y2 and above the plane z = 2y is ______ . Correct answer is '1.570'. Can you explain this answer?

Consider the region D in the yz plane bounded by the line y = 1/2 and the curve y2 z2 = 1, where y≥0. If the region D is revolved about the R3 z-axis in ¹, then the volume of the resulting solid is: а) л//3 b) 2π//3 c) π/3/2 d) π√3?

The volume of the solid bounded by the surfaces x=1-y^{2} and x=y^{2}-1 and the planes z=0 and z=2 (round off to 2 decimal places) is?

Top Courses for Mathematics

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams