Question

Consider a triangle ABC with AB = 2, BC = 5, and AC = 6. If the triangle is rotated around AB, what is the volume of the solid that is generated?

Answer 1

Answer:

The volume of the solid generated is 52.33 cubic units.

Step-by-step explanation:

Given the triangle ABC

• AB = 2

• BC = 5

• AC = 6

If the ABC triangle is rotated around AB, it would generate a circular cone. The volume of the generated cone can be computed using the following formula.

$V=\frac{1}{3}\pi r^{2} h$

From the given triangle,  

• AB = height = 2

• BC = radius = 5

So,  

Putting these values in $V=\frac{1}{3}\pi r^{2} h$ would yield the volume of a circular cone.

$V=\frac{1}{3}\pi r^{2} h$

$V=\frac{1}{3}(3.14) (5)^{2} (2)$

$V=52.33$

Therefore, the volume of the solid generated is 52.33 cubic units.

Keywords: triangle, volume, solid, right circular cone

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