The surface area of a cone is divided into two parts.A standard formula can be used to find the total surface area if you know the base and cone's slant heights.You might have the height or volume of the cone, as well as the radius.The volume formula and the Pythagorean Theorem can be used to derive the slant height and surface area of the cone.
Step 1: The formula should be used for the surface area of the cone.
SAdisplaystyle text is where the formula is.The total surface area of a cone is equal to the sum of the two parts.The slant height is the distance between the top of the cone and the base.The height is the distance between the top and the base, not the slanted height.
Step 2: The formula should have the value of the radius plugged into it.
You should be able to measure this length.Substitute for the displaystyle r variables in the formula.If the base of a cone is less than 5 cm, your formula will look like this.
Step 3: The value of the slant height is plugged into the formula.
You should be able to measure this length.If the slant height of the cone is 10 cm, your formula will look like this.
Step 4: Determine the surface area of the cone.
If you want to do this, you have to take the radius, slant height, and displaystyle.If you don't use a calculator, use 3.14 as the displaystyle.For example, SA is for SA(10)+(pi )(52)
Step 5: The area of the cone's base is calculated.
If you want to do this, you have to square the base's radius.If you're not using a calculator, use 3.14 as the displaystyle.SA=157+(pi )(52) is a displaystyle for example.
Step 6: Add the base area of the cone.
The total surface area is in square units.The surface area of a cone with a radius of 5 cm and a slant height of 10 cm is 235.5 square centimeters.
Step 7: The formula for the Pythagorean Theorem needs to be set up.
The side lengths of a right triangle are equal to the displaystyle a and b.The height of the cone should not be confused with the slant height, which is the diagonal distance from the top to the base.The height is the distance from the top to the base.
Step 8: The height and length should be plugged into the formula.
The two sides of a right triangle are the radius and height of the cone.Substitute the height for the variable bdisplaystyle b.If the height of the cone is 12 cm and the radius is 5 cm, your formula will look like this: 52+122.
Step 9: Then add the lengths of the radius and height.
Squared a number means to multiply it by itself.For example:52+122 is a displaystyle of 52+122.
Step 10: Take the root of the equation.
The hypotenuse of the right triangle is the same as the slant height.The slant height of this example is 13
Step 11: The formula should be used for the surface area of the cone.
Where SAdisplaystyle text is found is in the formula.The base area and the total surface area of a cone are the same.
Step 12: The known values should be put into the formula.
You already calculated the slant height by giving the radius.Don't use the perpendicular height in the surface area formula.If you don't use a calculator, use 3.14 for displaystyle pi for example, for a cone with a radius of 5 cm and a slant height of 13 cm.
Step 13: To find the base area, you have to multiply.
Add the products together.You will get the total surface area in square units with the sum.SA=204.1+(3.14)(25) is a example.
Step 14: The formula for the volume of a cone should be set.
The formula is V=13()(r2)(h)displaystyle V, where V equals the volume of the cone.The height of the cone should not be confused with the slant height, which is the diagonal distance from the top to the base.The height is the distance between the top and the base.
Step 15: The known values can be plugged into the formula.
You should know how long the radius is.You can't use this method if you're not sure.If you don't use a calculator, use 3.14 for displaystyle.If you know the volume and radius of the cone, your formula will look like this.
Step 16: The multiplication needs to be completed.
First, square the radius, and then use the displaystyle pi to add up the value.Then, divide that product by 13.This will give you the coefficients for the variables.For example_950=13(3.14)(62)(h)displaystyle
Step 17: The h coefficient is used to divide the side by side.
The value of displaystyle h is the height of the cone.The information you need to find the slant height of the cone is here.There is a displaystyle of 95037.68 that is used for example.
Step 18: The formula for the Pythagorean Theorem needs to be set up.
The side lengths of a right triangle are equal to the displaystyle of the formula.
Step 19: Plug the height and length into the formula.
The two sides of a right triangle are determined by the radius and height of the cone.For example, if the cone is 6 cm and the height is 25.21 cm, your formula will look like this: 62+25.212
Step 20: There is a solution for displaystyle c.
The length of the right triangle's hypotenuse is the same as the slant height.For example:62+25.212 is a displaystyle.
Step 21: The formula should be used for the surface area of the cone.
SAdisplaystyle text is where the formula is.The base area and the total surface area of a cone are the same.
Step 22: The known values should be put into the formula.
The surface area formula should use the slant height, not the perpendicular height.If you don't use a calculator, use 3.14 for displaystyle pi for example, for a cone with a radius of 6 cm and a slant height of 25.91 cm.
Step 23: To find the base area, you have to multiply.
Add these products together.The total surface area of the cone will be given by the sum.There is a display style called "text" for example.