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The triangular region is rotated around the X-axis. What are the name and dimensions of the solid that is created from the rotation

The triangular region is rotated around the X-axis. What are the name and dimensions-example-1
User Madmenyo
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1 Answer

27 votes
27 votes

Answer:

  • cone
  • radius 8 units
  • height 6 units

Explanation:

The attached image shows the figure of rotation generated by rotating a triangular shape about the x-axis.

Shape

When the given line is rotated about the x-axis, each point on the line traces a circle in the y-z plane. Those together will make a cone shape. The radius of the circle is the distance of the point from the x-axis.

Dimensions

The base of the cone will be the circle obtained by rotating the y-intercept about the x-axis. As above, the radius of that circular base is the y-value of the y-intercept: 8 units.

The height of the cone will be the x-value of the point where the radius is zero, at x=6.

The cone has a height of 6 units and a radius of 8 units.

The triangular region is rotated around the X-axis. What are the name and dimensions-example-1
User Jimbobuk
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2.8k points