If a cylinder’s radius and height are each shrunk down to a third of the original size, what would be the formula to find the modified surface area?
a = 2pi r (r+h)
If r and h are shrunk by a factor of 3 each, than we have
2pi (r/3)(r/3 + h/3) = 2/9 pi r (r+h) = 1/9 a
as with all geometric figures, when the linear dimensions are scaled by a factor of f, the area is scaled by f^2 and the volume is scaled by f^3.
To find the modified surface area of a cylinder when both the radius and height are shrunk down to a third of the original size, you can use the formula for the surface area of a cylinder.
The formula for the surface area of a cylinder is given by:
Surface Area = 2πrh + 2πr^2
Where:
- π is a mathematical constant approximately equal to 3.14159
- r is the radius of the cylinder
- h is the height of the cylinder
Now, if the radius and height are each shrunk down to a third of the original size, you need to calculate the new values of the radius and height and substitute them into the formula.
Let's say the original radius is 'r' and the original height is 'h'.
The modified radius would be (1/3) * r, and the modified height would also be (1/3) * h.
Using the modified values, the formula for the modified surface area of the cylinder becomes:
Modified Surface Area = 2π((1/3) * r)((1/3) * h) + 2π((1/3) * r)^2
Simplifying this equation further, the modified surface area is:
Modified Surface Area = (2/9)πrh + (2/9)πr^2
So, the formula to find the modified surface area of the cylinder with a shrunk radius and height is (2/9)πrh + (2/9)πr^2.