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Find the volume of the tetrahedron, if lengths of two opposite sides are 2 and 4 respectively and the shortest distance between them is 6 and these sides are inclined at 30º.
Correct answer is '4'. Can you explain this answer?
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Find the volume of the tetrahedron, if lengths of two opposite sides a...
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Find the volume of the tetrahedron, if lengths of two opposite sides a...
To find the volume of a tetrahedron, we need to know the lengths of all its sides or the lengths of two opposite sides and the angle between them. In this case, we are given the lengths of two opposite sides (2 and 4) and the angle between them (30 degrees).
To find the volume, we can use the formula:
Volume = (1/6) * base area * height
First, let's find the base area. The base of the tetrahedron is an equilateral triangle with side length 2. We can find the area of an equilateral triangle using the formula:
Area = (sqrt(3) / 4) * side^2
Area = (sqrt(3) / 4) * 2^2
= (sqrt(3) / 4) * 4
= sqrt(3)
Next, let's find the height of the tetrahedron. The height is the shortest distance between the two opposite sides, which is given as 6.
Now, we can calculate the volume:
Volume = (1/6) * base area * height
= (1/6) * sqrt(3) * 6
= sqrt(3)
Therefore, the volume of the tetrahedron is sqrt(3) cubic units.
To find the volume, we can use the formula:
Volume = (1/6) * base area * height
First, let's find the base area. The base of the tetrahedron is an equilateral triangle with side length 2. We can find the area of an equilateral triangle using the formula:
Area = (sqrt(3) / 4) * side^2
Area = (sqrt(3) / 4) * 2^2
= (sqrt(3) / 4) * 4
= sqrt(3)
Next, let's find the height of the tetrahedron. The height is the shortest distance between the two opposite sides, which is given as 6.
Now, we can calculate the volume:
Volume = (1/6) * base area * height
= (1/6) * sqrt(3) * 6
= sqrt(3)
Therefore, the volume of the tetrahedron is sqrt(3) cubic units.
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Find the volume of the tetrahedron, if lengths of two opposite sides are 2 and 4 respectively and the shortest distance between them is 6 and these sides are inclined at 30º.Correct answer is '4'. Can you explain this answer?
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Find the volume of the tetrahedron, if lengths of two opposite sides are 2 and 4 respectively and the shortest distance between them is 6 and these sides are inclined at 30º.Correct answer is '4'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Find the volume of the tetrahedron, if lengths of two opposite sides are 2 and 4 respectively and the shortest distance between them is 6 and these sides are inclined at 30º.Correct answer is '4'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the volume of the tetrahedron, if lengths of two opposite sides are 2 and 4 respectively and the shortest distance between them is 6 and these sides are inclined at 30º.Correct answer is '4'. Can you explain this answer?.
Find the volume of the tetrahedron, if lengths of two opposite sides are 2 and 4 respectively and the shortest distance between them is 6 and these sides are inclined at 30º.Correct answer is '4'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Find the volume of the tetrahedron, if lengths of two opposite sides are 2 and 4 respectively and the shortest distance between them is 6 and these sides are inclined at 30º.Correct answer is '4'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the volume of the tetrahedron, if lengths of two opposite sides are 2 and 4 respectively and the shortest distance between them is 6 and these sides are inclined at 30º.Correct answer is '4'. Can you explain this answer?.
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