Surface Area of a Cone Calculator

Make use of this handy Surface Area of a Cone Calculator tool to get the total surface area, curved surface area of a cone in split of seconds. Just provide radius and slant height of the cone in the offered input fields and hit on the calculate button to acquire the output easily.

Surface Area of a Cone Calculator: Learning surface area of geometric shapes is become necessary for every student. You may feel that the entire process to compute the cone surface area is boring and time consuming at times. To help you out in such scenarios we have come up with an free online tool that does your math calculations instantaneously. Make your calculations accurate, easy, and get the entire process in detail.

How to Find Surface Area of a Cone?

Take the help of simple and easy guidelines listed below and know the procedure on steps to get curved surface area, total surface area of a cone manually. They are along the lines

  • As a first step, take the slant height and radius of the curved cone.
  • Remember that all those values should be in same units.
  • If any one of them is having different units, then convert it.
  • Surface area of cone A = π r (l + r)
  • Place the values in the above formula.
  • Perform the required math arithmetical operations to get the accurate answer.

Surface Area of Cone Formula

Cone is a three dimensional solid figure having circular base. It moves smoothly from the circular base to the point of called apex. The body of the cone has a curved surface. The formula to find the surface area of a cone is given below:

Curved Surface area of cone = π r l sq units

Total surface area of cone = π r (l + r) sq units

Right circular cone surface area = π r (r + √h2 + r2)

Where,

r is the radius of the circular base

h is height of the cone

l is the slant height of the cone.

Example

Question: Calculate the Total surface area of a cone whose radius is 8 cm and height is 12 cm?

Solution:

Given that,

r = 8 cm

h = 12 cm

l = √h2 + r2

= V122 + 82

= V144 + 64

= √208 = 14.42

Total surafce area A = π r (l + r)

= π * 8 (14.42 + 8)

= π * 8 (22.42)

= 3.14 * 8 * 22.42

= 563.7 cm2.

Hence, total surface area is 563.7 cm2.

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Surface Area of a Cone Calculator

FAQs on Surface Area of a Cone Calculator

1. How do you find the slant height of a cone?

We draw a right angled triangle taking base, slant height and height as the side. By using the Pythagorean theorem, sum of the squares of the sides is equal to the hypotenuse square. So, slant height2 = radius2 + height2.


2. What is the difference between slant height and height of a cone?

These two are the dimensions of a cone. Vertical height is a straight line that joins apex and mid point of the circular base. Slant height connects the apex and any edge point on the circle.


3. How do you find the surface area of a cone without the slant height?

The formula to find the surface area of a cone without knowing its slant height is A = π r (r+ √h2+r2). Where r, h are the radius and height of the cone. Substitute the values and do math calculations to get the result.


4. Determine the curved surface area of a cone whose base radius is 7 cm and slant height is 15 cm?

Curved surface area of a cone = π r l

= (22/7) * 7 * 15

Curved surface area of a cone = 330 cm2