Total surface area of a cone
The total surface area of a cone is the area of its curved surface plus the area of its circular base.
In one line: Cone total means curved side plus base.
Practice This ConceptUnderstand it
A cone has one circular base and one curved sloping face. When the entire outer surface is required, both parts must be counted. The base area is added to the curved surface area, which gives the standard total surface area formula.
Example
Formula and rule
Total surface area of a cone = πr(l+r), where r is the radius and l is the slant height.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
For r = 3 cm and l = 5 cm, TSA = πr(l+r) = π × 3 × 8 = 24π cm².
Method you can reuse
- 1Confirm that the whole outer surface is required.
- 2Write TSA = πr(l+r).
- 3Substitute r and l.
- 4Simplify carefully.
- 5Present the answer in square units.
Sketch it in your answer
Draw the cone with the circular base clearly marked and the slant height on the side. Show that the outside area is the curved face plus the base circle.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
A conical tent is to be covered on the outside, including its base rim. Which formula should be used?
Think first, then show answerHide answer
Common wrong answer
A common wrong answer is πrl. That gives only the curved surface area and leaves out the circular base.
Don't mix this up
Exam tip
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
The total surface area of a cone is the area of its curved surface plus the area of its circular base.
- 2
Add for 2 marks
Example: If a cone has radius 3 cm and slant height 5 cm, TSA = πr(l+r) = π × 3 × (5+3) = 24π cm².
- 3
Add for 3 marks
When the entire outer surface is required, both parts must be counted.
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