AI generatedGeometry and measuresCourse skill

Finding a cone's perpendicular height from its slant height

Finding a cone's perpendicular height from its slant height.

  • Split a compound solid into familiar shapes.
  • Use perpendicular height for volume and slant height for a cone’s curved area.
  • Add volumes, or subtract a removed part. Give cubic units.

Example 1

The cone has radius 3 cm and slant height 5 cm. Find its perpendicular height.

Right triangle through the cone axis; lengths in cmOBADiagram not to scale
Subtract the radius squared from the slant height squared.Take the positive square root.

Example 2

The cone has radius 6 cm and slant height 10 cm. Find its perpendicular height.

Right triangle through the cone axis; lengths in cmOBADiagram not to scale
Subtract the radius squared from the slant height squared.Take the positive square root.

Your turn

Question 1

The cone has radius 9 cm and slant height 15 cm. Find its perpendicular height.

Right triangle through the cone axis; lengths in cmOBADiagram not to scale
Check answer
Subtract the radius squared from the slant height squared.Take the positive square root.
Question 2

The cone has radius 12 cm and slant height 20 cm. Find its perpendicular height.

Right triangle through the cone axis; lengths in cmOBADiagram not to scale
Check answer
Subtract the radius squared from the slant height squared.Take the positive square root.
Question 3

The cone has radius 15 cm and slant height 25 cm. Find its perpendicular height.

Right triangle through the cone axis; lengths in cmOBADiagram not to scale
Check answer
Subtract the radius squared from the slant height squared.Take the positive square root.
Question 4

The cone has radius 18 cm and slant height 30 cm. Find its perpendicular height.

Right triangle through the cone axis; lengths in cmOBADiagram not to scale
Check answer
Subtract the radius squared from the slant height squared.Take the positive square root.
Question 5

The cone has radius 3 cm and slant height 5 cm. Find its perpendicular height.

Right triangle through the cone axis; lengths in cmOBADiagram not to scale
Check answer
Subtract the radius squared from the slant height squared.Take the positive square root.
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