the ? says "a cone has the surface area of 160 sq. in. If the dimensions are reduced by 1/2,what is the surface area of the new cone?" i just cant seem to find the formula for the surface area of the cone.
Check this site.
http://math.about.com/od/formulas/ss/surfaceareavol_2.htm
Surface area cone:
TOP: 1/2 (circumfirance of bottom x height)
= 1/2 (PI*radius x height)
So if you ignore the bottom of the cone, then reducing the dimensions by 1/2...
thanks for helping me
To find the formula for the surface area of a cone, you need to know its radius and slant height. The formula for the surface area of a cone is given by:
Surface Area = π * r * (r + l)
Where:
- π (pi) is a mathematical constant approximately equal to 3.14
- r is the radius of the cone's base
- l is the slant height of the cone
Now, let's solve the problem. We are given that the surface area of the original cone is 160 sq. in. If the dimensions are reduced by 1/2, we need to figure out the new dimensions and find the surface area of the new cone.
Let's assume the original cone has a radius of R and a slant height of L. So, the surface area of the original cone can be written as:
160 = π * R * (R + L)
Next, we need to find the new dimensions. Since they are reduced by 1/2, we multiply the original radius (R) and slant height (L) by 1/2. The new radius will be R/2 and the new slant height will be L/2.
Now, we can calculate the surface area of the new cone using the same formula:
Surface Area (new) = π * (R/2) * [(R/2) + (L/2)]
To simplify further:
Surface Area (new) = π * (R/2) * (R + L) / 2
Surface Area (new) = π * R * (R + L) / 4
So, the surface area of the new cone is π * R * (R + L) / 4.