# Surface Area of a Cone Calculator

**Surface Area of Cone -**The surface area of a cone is equal to the area of the base plus the area of the cone.

**Here are some samples of Surface Area of a Cone calculations**

**Surface Area of a Cone Calculator:** It is a free online tool that provides the output when given radius and height value. Surface Area of a Cone Calculator makes calculations easier for you by giving outputs in a fraction of seconds. Below we will explain how to use our surface area of a cone calculator and what is meant by the surface area of a cone and how to calculate it.

## What is meant by the Surface Area of a Cone Calculator?

Cone is a three-dimensional solid figure having a circular base. It tapers from a circular base to the point called the apex. Usually, the cone body has a curved surface. Surface Area of a Cone is the summation of the area of base and area of the cone.

If "r" is the radius and "h" is the height of the cone and the formula to calculate the Surface Area of Cone is given in the further modules.

Surface Area of Cone A = πr(r + √(h² + r²))

### How to find the Surface Area of a Cone?

You can calculate the surface area of a cone based on the parameters. We tried explaining it in a clear way by taking enough worked out examples. Have a glance at them and know the method approached to arrive at the solution.

If you are given the radius and slant height value then Surface of a Cone is given by the following formula

** Surface Area of Cone A = πr(l+r) Sq. Units**

In the other case when you are given the radius and height are known formula to calculate the surface area of a cone is given by

** Surface Area of Cone A = πr(r + √(h² + r²))**

Hope you got an idea on how to find the surface area of a calculator and the equations powered to find it. Let me explain in detail by taking some enough examples so that you will be familiar with the surface area of a cone concept even better.

**Example 1**

Find the Surface area of a cone when the radius is 8 cm and height is 10 cm?

**Solution:**

Surface Area of a Cone is the summation of the Area of cone and Area of the base.

Given that Base Radius (r) = 8 cm

Height(h)= 10 cm

Substitute the values in the formula A = πr(r + √(h² + r²))

i.e. A = π8(8+√(10² + 8²))

On simplifying further we get as such A = π8(8+ √(100+64))

= π8(8+ √ (164))

Substitute the value of π = 3.14 and then the mathematical equation will turn into as such

A= 3.14*8(8+√(164))

= 522.6529617 Cm^{2}

**Example 2 **

Find the surface area of the cone if the radius is 5 cm and the slant height is 15 cm?

**Solution:**

Surface Area of a Cone if the slant height is given is A = πr(r + l)

Given Slant height l =15 cm

Radius(r) = 5 cm

Substitute them in the formula and on doing so we will get as such

A = π5(5+15)

= π5(20)

=100π

=100(3.14)

= 314 cm^{2}

### How to use Surface Area of a Cone Calculator?

Follow the simple steps on how to find the Surface Area of a Cone using our handy calculator. Use this simple tool and calculate the make your calculations faster. They are as follows

- Fill up the value of base radius and height in the inputs.
- Select the input metric be it cm, m, ft, yd, mi, etc. and then click on the Area Button.
- Finally, you will be displayed with the surface area of the cone in the output.

### FAQs on Surface Area of a Cone

**1. What is meant by the Surface Area of a Cone?**

Surface Area of a Cone is the summation of the area of base and area of the cone.

**2. How do you find the surface area of a cone?**

You can find the surface area of a cone using our calculator and get the output in a fraction of seconds.

**3. What is the formula of the surface area of a cone?**

The formula for the surface area of a cone is πr(r + √(h² + r²)) in which r is the radius and h is the height.

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

The vertical height (or altitude) is the perpendicular distance from the top down to the base. The slant height is the distance from the top, down the side, to a point on the base circumference.