Question

In the triangle AC=6in and BC=7in. Triangle ABC is rotated about segment BC. Determine the volume of the solid formed by the rotation.

Answer 1

Given: A right triangle ABC

To Determine: The volume of the solid formed if rotated about the segmented BC

Solution

A right circular cone is generated by rotating a right-angled triangle about one of the sides containing the right angle. When we take one side of the right angle as the base and the side perpendicular, as the center and rotate the triangle, it forms a right circular cone.

For the given triangle, we have

So, the new solid is a cone. The volume of a cone is calculated by the formula

`\begin{gathered} V_(cone)=(1)/(3)\pi r^2h \\ r=AC=6in \\ h=BC=7in \end{gathered}`

Therefore:

`\begin{gathered} V_(cone)=(1)/(3)*\pi*7^2*6 \\ V_(cone)=\pi*49*2 \\ V_(cone)=98\pi in^3 \\ V_(cone)=307.876in^3 \\ V_(cone)\approx308in^3 \end{gathered}`

Hence, the volume of the solid to the nearest integer is 308 in³