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Total surface area of a Frustum of a Cone
TSA = πl(R + r) + πR² + πr²
Where: R = bottom radius, TSA = Total surface area, l = slant height, r = top radius
Use the same units for all lengths (e.g. all in cm); areas come out in cm², volumes in cm³.
Solved example
Given: R = 7, l = 5, r = 10
Find: TSA_ (Total surface area)
- Formula: TSA = π·R² + π·l·(R + r) + π·r²
- Substitute the values: TSA = π·10² + π·5·(10 + 7) + π·7²
- Result: TSA = 735.132681
Answer: TSA_ = 735.132681
Calculator
How to calculate Total surface area of a Frustum of a Cone
- Write down the formula: TSA = πl(R + r) + πR² + πr².
- Note the known values (R, l, r).
- Substitute them and simplify to find TSA_.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for Total surface area of a Frustum of a Cone?
The formula is TSA = πl(R + r) + πR² + πr², where R = bottom radius, TSA = Total surface area, l = slant height, r = top radius.
What is Total surface area of a Frustum of a Cone when R = 7, l = 5, r = 10?
TSA_ = 735.132681. Substitute the values into TSA = πl(R + r) + πR² + πr² and simplify.