Welcome to our Area of a Cone Calculator page.

We explain how to find the surface area of a right cone and provide a quick calculator to work it out for you, step-by-step.

The calculator will also find the area of an open cone with no base.

Quicklinks to ...

Our calculator finds the surface area of a right circular cone when the radius (or diameter) and height are known.

- Select the type of cone you want: closed or open (default is closed).
- Select if you want to use the radius or diameter (default is radius).
- For the value, you can choose a whole number, decimal or fraction.
- You can type a fraction by typing the numerator then '/' then the denominator.
- You can type a mixed number by typing the whole-number part, then a space then the fraction part.
- Examples: 2 1/2 (two and one-half); 3 4/5 (three and four-fifths); 7 1/3 (seven and one-third).

- Choose your units of measurement (default is none)
- Choose your desired accuracy (default is 2 decimal places)
- Click the Find Area button
- You will be given two answers for the area, one in terms of Pi (π) and the other answer as a decimal value.

There are many different types of cones, including right cones, oblique cones and elliptic cones.

The cones that are most common, and that we use for our area of a cone calculator, are right circular cones, which is a cone with a circular base whose apex (highest point) is directly above the center of the base.

As well as different types of cones, there are also categories of cone within each type: open and closed cones

A closed cone has two surfaces which includes a base (or top depending on which way up it is).

An open cone is just a curved surface with no base (or top).

The surface area of a closed cone is: \[ A = \pi r (r + \sqrt {r^2 + h^2} \; ) \]

The surface area of an open cone is: \[ A = \pi r \sqrt {r^2 + h^2} \]

where r is the radius of the circle and h is the perpendicular height of the cone.

Find the area of the closed cone below. Give your answer to 1 decimal place.

The height of the cone is 12 cm. The radius is 5 cm.

The formula for the area of a closed cone is: \[ A = \pi r (r + \sqrt {r^2 + h^2} \; ) \]

If we substitute the values of the radius and height into the formala, we get: \[ A = \pi \cdot (5) \cdot (5 + \sqrt {5^2 + 12^2} \; ) \]

If we simplify this, we get: \[ A = 5 \pi \cdot (5 + \sqrt {25 + 144}) = 5 \pi \cdot (5 + \sqrt {169} \;) \]

This means that: \[ A = 5 \pi \cdot (5 + 13) = 5 \pi \cdot (18) = 90 \pi \]

This gives us a final answer of: \[ A = 282.7 \;\ cm^2 \;\ to \;\ 1 \;\ decimal \;\ place \]

Find the surface area of the closed cone below to 1 decimal place.

The cone is lying on its side. The actual height of the cone is 8 inches. The radius is 3 ½ inches.

The formula for the area of a closed cone is: \[ A = \pi r (r + \sqrt {r^2 + h^2} \; ) \]

If we substitute the values of the radius and height into the formala, we get: \[ A = \pi \cdot (3 {1 \over 2}) \cdot (3 {1 \over 2} + \sqrt {(3 {1 \over 2})^2 + 8^2} \; ) \]

If we simplify this, we get: \[ A = 3 {1 \over 2} \pi \cdot (3 {1 \over 2} + \sqrt {12 {1 \over 4} + 64} \; ) = 3 {1 \over 2} \pi \cdot (3 {1 \over 2} + \sqrt {76 {1 \over 4}} \; ) \]

This means that: \[ A = 3 {1 \over 2} \pi \cdot (3 {1 \over 2} + 8.732...) = 3 {1 \over 2} \pi \cdot (12.232...) = 42.812... \pi \]

This gives us a final answer of: \[ A = 134.5 \;\ in^2 \;\ to \;\ 1 \;\ decimal \;\ place \]

Find the surface area of the closed cone below to 2 decimal places.

The height of the cone is 4.8 meters. The diameter of the cone is 4.6 meters.

To find the radius, we divide the diameter by 2. So the radius = 4.8 ÷ 2 = 2.4 meters.

The formula for the area of a closed cone is: \[ A = \pi r (r + \sqrt {r^2 + h^2} \; ) \]

If we substitute the values of the radius and height into the formala, we get: \[ A = \pi \cdot (2.4) \cdot (2.4 + \sqrt {(2.4)^2 + (4.6)^2} \; ) \]

If we simplify this, we get: \[ A = 2.4 \pi \cdot (2.4 + \sqrt {5.76 + 21.16} \; ) = 2.4 \pi \cdot (2.4 + \sqrt {26.92} \; ) \]

This means that: \[ A = 2.4 \pi \cdot (2.4 + 5.1884...) = 2.4 \pi \cdot (7.588...) = 18.212... \pi \]

This gives us a final answer of: \[ A = 57.22 \;\ m^2 \;\ to \;\ 2 \;\ decimal \;\ places \]

Find the surface area of the witch's black hat which is an open cone shown below. Give your answer to 1 decimal place.

The height of the cone is 60 cm. The diameter of the cone is 18 cm.

To find the radius, we divide the diameter by 2. So the radius = 18 ÷ 2 = 9 cm.

The formula for the area of an open cone is: \[ A = \pi r \sqrt {r^2 + h^2} \]

If we substitute the values of the radius and height into the formala, we get: \[ A = \pi \cdot (9) \cdot \sqrt {9^2 + 60^2} \]

If we simplify this, we get: \[ A = 9 \pi \cdot \sqrt {81 + 3600} = 9 \pi \cdot \sqrt {3681} \]

This means that: \[ A = 9 \pi \cdot (60.671...) = 546.041... \pi \]

This gives us a final answer of: \[ A = 1715.4 \;\ cm^2 \;\ to \;\ 1 \;\ decimal \;\ place \]

We have created two worksheets for you to practice the skill of finding the area of a range of different closed and open cones.

Sheet 1: you have to find the area of different closed cones using the height and radius or diameter measurements.

Sheet 2: you have to find the area of different open and closed cones using the height and radius or diameter measurements.

You can use our area of a cone calculator to check you working out if you get stuck!

Take a look at some more of our worksheets similar to these.

We also have a volume of a cone calculator which works in a similar way to the calculator on this page.

We have a range of area and volume calculators to help you find the area and volumes of a range of different 2d and 3d shapes.

Each calculator page comes with worked examples, formulas and practice worksheets.

We have a range of other area worksheets and support pages for a range of different 2d shapes.

We have a wide range of free math calculators to help you.

Most of our calculators show you their working out so that you can see exactly what they have done to get the answer.

Our calculator hub page contains links to all of our calculators!

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