This calculator helps you find the total surface area of a cone, which includes the area of its circular base and its curved lateral surface. Just enter the radius and the slant height, and we'll do the math for you.
The distance from the center of the base to its edge.
The distance from the apex (tip) of the cone to any point on the circumference of its base.
This calculator helps you find the total surface area of a cone, which includes the area of its circular base and its curved lateral surface. Just enter the radius and the slant height, and we'll do the math for you.
Total Surface Area = πr(r + s) Where: π (Pi) ≈ 3.14159 r = radius of the base s = slant height of the cone
Imagine a cone with a base radius (r) of 3 cm and a slant height (s) of 5 cm. Using the formula, Total Surface Area = π * 3 * (3 + 5) = π * 3 * 8 = 24π ≈ 75.398 cm². This tool will show you this result clearly.
The surface area of a cone is the total area of its outer surfaces. For a right circular cone, this includes the area of its circular base and the area of its curved side (lateral surface).
If you know the cone's height (h) and radius (r), you can find the slant height (s) using the Pythagorean theorem: s = √(r² + h²). The height, radius, and slant height form a right-angled triangle inside the cone.
The total surface area formula combines two parts: the area of the circular base (πr²) and the lateral (curved) surface area (πrs). Adding these together gives πr² + πrs, which can be factored as πr(r + s).
Cone Surface Area Calculator: Master the Formula and Examples
Understanding the surface area of a cone is a common task in geometry, whether you're tackling school homework or working on a design project. A cone's surface area tells you the total space covered by its outer layer, including its circular base and its curved side. This guide will walk you through the essential formula and demonstrate how to use our Cone Surface Area Calculator to get quick, accurate results.
A cone is a three-dimensional geometric shape that tapers smoothly from a flat circular base to a point called the apex or vertex. Its surface area is made up of two main parts: the area of its circular base and the area of its lateral (curved) surface. The formula for the total surface area of a right circular cone is given by: Total Surface Area = πr(r + s). Here, 'π' (Pi) is a mathematical constant approximately equal to 3.14159. 'r' represents the radius of the cone's base, which is the distance from the center of the base to any point on its circumference. 's' stands for the slant height, which is the distance from the apex of the cone down to any point on the circumference of the base, measured along the surface of the cone. If you only know the perpendicular height (h) of the cone, you can find the slant height using the Pythagorean theorem: s = √(r² + h²).
The formula for the total surface area of a cone is: Total Surface Area = πr² + πrs Which can also be written as: Total Surface Area = πr(r + s) Where: π ≈ 3.14159 r = radius of the base s = slant height
Let's say you have a cone-shaped party hat with a base radius of 7 cm and a slant height of 10 cm. To find the total surface area, we use the formula: Total Surface Area = π * 7 * (7 + 10) = π * 7 * 17 = 119π. If we use π ≈ 3.14159, the total surface area is approximately 373.85 cm². This includes the area of the circular opening at the bottom (if it were covered) and the curved paper of the hat itself.
Using the ProMathTools Cone Surface Area Calculator is straightforward. Simply enter the 'Radius (r)' of your cone's base into the first input field. Then, enter the 'Slant Height (s)' into the second field. Make sure both measurements are in the same units. Once you've entered the values, the calculator will instantly display the base area, lateral surface area, and the total surface area, giving you a clear breakdown of the results.
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