# Develop a formula for the SA of a cone

In summary: Would that be the proper thing for S?Yes, ##s=\sqrt{h^2+r^2}## and you have ##h = 6r##. Put that in for the ##h## in the ##s## equation. Then put that result in for the ##s## in your SA equation. Then solve that for ##r##.

## Homework Statement

Develop a formula for radius as a function of surface area for a cone with height three times its diameter.

∏rs + ∏r^2 = SA
s = √(h^2+r^2)
H = 3d or 6r

## The Attempt at a Solution

Dont know what values to use for s = √(h^2+r^2).

Last edited:

## Homework Statement

Develop a formula for radius as a function of surface area for a cone with height three times its diameter.

∏rs + ∏r^2 = SA
s = √(h^2+r^2)
3h=1d or 2r

## The Attempt at a Solution

Dont know what values to use for s = √(h^2+r^2).

You are given that the height is 3 times the diameter, so you can get s in terms of r. Put that in your formula for SA and solve for r in terms of SA.

LCKurtz said:
You are given that the height is 3 times the diameter, so you can get s in terms of r. Put that in your formula for SA and solve for r in terms of SA.

Would my h value be 3 and my r value be 0.5 ?

I also realized I made the error 3D=1H instead of vice versa.

Would my h value be 3 and my r value be 0.5 ?

No, ##r## isn't given. It is one of the variables you are to use. It and SA are the variables in your requested equation. ##H = 3D = 6r##.

blah

I derived r = √(s^2-h^2)/6. Can you check that ?

Why bother with that? You need s in terms of r to plug into your SA equation.

s=√(h^2+6r^2), the answer is r=√SA/∏(1+√37). How do they get rid of the H ?

LCKurtz said:
Why bother with that? You need s in terms of r to plug into your SA equation.

Would that be the proper thing for S?

You have ##s=\sqrt{h^2+r^2}## and you have ##h = 6r##. Put that in for the ##h## in the ##s## equation. Then put that result in for the ##s## in your SA equation. Then solve that for ##r##.

## What is the formula for the surface area of a cone?

The formula for the surface area of a cone is A = πr(r + √(h^2 + r^2)), where A represents the surface area, r represents the radius of the base, and h represents the height of the cone.

## How do you calculate the radius of a cone?

The radius of a cone can be calculated by dividing the diameter of the base by 2, or by using the formula r = √(A/π - h^2), where A represents the surface area and h represents the height of the cone.

## What units are used for the measurements in the formula?

The units used for the measurements in the formula for the surface area of a cone can vary depending on the specific measurements used. However, the most common units are centimeters (cm) or meters (m) for length and square units such as square centimeters (cm^2) or square meters (m^2) for area.

## What is the difference between a cone and a cylinder?

A cone is a three-dimensional shape with a circular base and a curved surface that tapers to a point at the top, while a cylinder is a three-dimensional shape with two circular bases that are parallel and a curved surface connecting them. Additionally, the formula for the surface area of a cone includes the slant height, while the formula for the surface area of a cylinder only includes the height.

## Can the formula for the surface area of a cone be used for any type of cone?

Yes, the formula for the surface area of a cone can be used for any type of cone, as long as the base is circular and the measurements are in the same units. This includes right cones, oblique cones, and truncated cones.

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