The volume of the three-dimensional object (cone) formed is equal to 32π cubic units.
How to determine the volume of the three-dimensional object?
In this scenario, the effect of rotating the right triangle around line segment AB would form a three-dimensional object known as a cone, with the following dimensions:
How to calculate the volume of a cone?
Mathematically, the volume of a cone can be calculated by using this formula:
V = 1/3 × πr²h
Substituting the given parameters into the formula, we have;
V = 1/3 × π × 4² × 6
V = π × 16 × 2
V = 32π cubic units.
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Complete Question:
In the diagram below, right triangle ABC has legs whose lengths are 4 and 6. What is the volume of the three-dimensional object formed by continuously rotating the right triangle around line segment AB?
(1) 32π
(2) 48π
(3) 96π
(4) 144π
