Volume of tetrahedron

Calculus Level 4

Find the volume of the tetrahedron with corners at ( 0 , 0 , 0 ) (0, 0, 0) , ( 0 , 3 , 0 ) (0, 3, 0) , ( 2 , 3 , 0 ) (2, 3, 0) , and ( 2 , 3 , 5 ) . (2, 3, 5).


The answer is 5.

Rahil Sehgal by Rahil Sehgal , 20, India

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1 solution

Tom Engelsman
May 22, 2017

The tetrahedron in question has a right-triangular base whose area equals 1 2 ⋅ ( 2 ⋅ 3 ) = 3 \frac{1}{2} \cdot (2 \cdot 3) = 3 square units. With a vertical height equal to 5 units, the volume now calculates to V = 1 3 ⋅ B ⋅ h = 1 3 ⋅ 3 ⋅ 5 = 5 V = \frac{1}{3} \cdot B \cdot h = \frac{1}{3} \cdot 3 \cdot 5 = \boxed{5} cubic units.

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