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What is the volume of the three-dimensional object formed by continuously rotating the right triangle around line segment AC

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Lanuel

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:

  • Radius, r = 4 units.
  • Height, h = 6 units.

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.

Read more on cone here: https://brainly.com/question/1082469

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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

View image Lanuel
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