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Finding a cone's slant height before its surface area

Finding a cone's slant height before its surface area.

  • Surface area counts only surfaces exposed on the outside.
  • Exclude faces where two solids join; include an exposed base.
  • For a cone, use the slant height in πrl. Give square units.

Example 1

Find the cone’s slant height, then its total surface area including its base. Give an exact area.

Right triangle through the cone axis; lengths in cmOBADiagram not to scale
The slant height is the hypotenuse.Take the positive square root.Add the curved surface and circular base.

Example 2

Find the cone’s slant height, then its total surface area including its base. Give an exact area.

Right triangle through the cone axis; lengths in cmOBADiagram not to scale
The slant height is the hypotenuse.Take the positive square root.Add the curved surface and circular base.

Your turn

Question 1

Find the cone’s slant height, then its total surface area including its base. Give an exact area.

Right triangle through the cone axis; lengths in cmOBADiagram not to scale
Check answer
The slant height is the hypotenuse.Take the positive square root.Add the curved surface and circular base.
Question 2

Find the cone’s slant height, then its total surface area including its base. Give an exact area.

Right triangle through the cone axis; lengths in cmOBADiagram not to scale
Check answer
The slant height is the hypotenuse.Take the positive square root.Add the curved surface and circular base.
Question 3

Find the cone’s slant height, then its total surface area including its base. Give an exact area.

Right triangle through the cone axis; lengths in cmOBADiagram not to scale
Check answer
The slant height is the hypotenuse.Take the positive square root.Add the curved surface and circular base.
Question 4

Find the cone’s slant height, then its total surface area including its base. Give an exact area.

Right triangle through the cone axis; lengths in cmOBADiagram not to scale
Check answer
The slant height is the hypotenuse.Take the positive square root.Add the curved surface and circular base.
Question 5

Find the cone’s slant height, then its total surface area including its base. Give an exact area.

Right triangle through the cone axis; lengths in cmOBADiagram not to scale
Check answer
The slant height is the hypotenuse.Take the positive square root.Add the curved surface and circular base.
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