When calculating the surface area of a 3D cone in Mathematics (Mensuration), you must know its Slant Height. It is a different measurement from the normal, straight height of the cone.
While the Slant Height is required to find the Surface Area, it is NOT used to find the Volume. The Volume of a cone (⅓ π r² h) only requires the normal perpendicular height (h).
Imagine an ice cream cone.
If you slice a cone in half right down the middle, you will see that the radius (r), the perpendicular height (h), and the slant height (l) form a perfect Right-Angled Triangle.
Therefore, we can easily find the slant height using the Pythagoras Theorem (Hypotenuse² = Base² + Perpendicular²):
l = √(r² + h²)
Where:
You cannot calculate the surface area of a cone using the normal height (h). You must use the slant height (l).
Using the formula l = √(r² + h²): l = √(3² + 4²) l = √(9 + 16) l = √25 = **5 cm**.
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