I fold a rectangular piece of plane paper into a circular fold. The radius of the circle along which fold is done is 2K cm. The length of unfolded dimension is M cm. I get a solid figure. What is the figure and what is its surface area (in cm2)?
I fold a rectangular piece of plane paper into a circular fold. The radius of the circle along which fold is done is 2K cm. The length of unfolded dimension is M cm. I get a solid figure. What is the figure and what is its surface area (in cm2)?
The correct option is B Cylinder,4πMK
On folding a Rectangle by circular fold, I get a circle which has a thickness. This is nothing but a cylinder. This can be understood by looking at figure below.
Now we need to surface area of cylinder. We use the methods mentioned in the previous question. We convert the 3-D surface into a 2-D planar surface. For this we need to unroll/unfold the cylinder to get back the rectangle plane piece which was used to make it.
The length of the circular fold is the length of the rectangle.
The length of circular fold = Circumference of circle
= 2π(radius of circle)
= 2π(2K)
= 4πK cm
Height of cylinder = Length of unfolded region = Breadth of rectangle
= M cm
Hence area of rectangular 2-D planar piece of paper = Length × Breadth
= 4πMK cm2
Cylinder,4πMK
On folding a Rectangle by circular fold, I get a circle which has a thickness. This is nothing but a cylinder. This can be understood by looking at figure below.
Now we need to surface area of cylinder. We use the methods mentioned in the previous question. We convert the 3-D surface into a 2-D planar surface. For this we need to unroll/unfold the cylinder to get back the rectangle plane piece which was used to make it.
The length of the circular fold is the length of the rectangle.
The length of circular fold = Circumference of circle
= 2π(radius of circle)
= 2π(2K)
= 4πK cm
Height of cylinder = Length of unfolded region = Breadth of rectangle
= M cm
Hence area of rectangular 2-D planar piece of paper = Length × Breadth
= 4πMK cm2
