what is the volume of box if volume of cylinder is 48.125 cubic cm, which formed by rolling a rectangular paper sheet along the length of the paper. if a cuboidal box (open lid) made from the same sheet of paper by cutting out the four square of the side 0.5 cm from each of the corners of the paper sheet then ?
gotta know the length of the cylinder or the radius. just having the volume doesn't tell us enough.
Hi Omkar, we do have a way for this question.Only way is to think out of the box. Let me tell you how it goes:
Volume of cylinder= (pi) (r)(r)(h)= 48.125
(r)(r)h = 15.3125
15.3125 is not a perfect square. To make it perfect square, h should be 5cm.
Now (r)(r)=15.3125/5 = 3.0625 which makes r = 1.75cm
Therefore, rectangular sheet has length of 2(pi)(r)=11cm and width (h) of 5cm.
After cutting a square of 0.5cm from each corner, the dimension of the cuboid becomes:
Length=11-1=10cm; Breadth=5-1=4cm; Height=0.5cm.
Therefore, Volume of cuboid= 10 x 4 x 0.5 = 20 cubic cm.
Thank you for reading it!
Have a nice day Omkar!
Jay Bankoti
Hi Omkar, we do have a way for this question.Only way is to think out of the box. Let me tell you how it goes:
Volume of cylinder= (pi) (r)(r)(h)= 48.125
(r)(r)h = 15.3125
15.3125 is not a perfect square. To make it perfect square, h should be 5cm.
Now (r)(r)=15.3125/5 = 3.0625 which makes r = 1.75cm
Therefore, rectangular sheet has length of 2(pi)(r)=11cm and width (h) of 5cm.
After cutting a square of 0.5cm from each corner, the dimension of the cuboid becomes:
Length=11-1=10cm; Breadth=5-1=4cm; Height=0.5cm.
T
To find the volume of the box made from the same sheet of paper, you need to follow these steps:
1. Calculate the dimensions of the rectangular paper sheet:
- Let the length of the rectangular paper sheet be "L" cm.
- Let the width of the rectangular paper sheet be "W" cm.
2. Calculate the dimensions of the cylinder formed by rolling the paper along its length:
- The circumference of the cylindrical base is equal to the length of the rectangular paper sheet. So, the circumference of the base is 2πr, where "r" is the radius of the cylinder.
- Therefore, 2πr = L.
- Solve this equation in terms of the radius "r": r = L/(2π).
- The height of the cylinder would be equal to the width of the rectangular paper sheet, which is "W".
3. Calculate the volume of the cylindrical paper sheet:
- The volume of a cylinder is given by V = πr²h, where "V" is the volume, "r" is the radius, and "h" is the height.
- Substituting the values, V = π(L/(2π))² × W = (L²W)/(4π).
4. Calculate the dimensions of the cuboidal box made by cutting squares from the corners:
- Since each side of the cut squares is 0.5 cm, the length and width of the cuboidal box would be:
- Length of the box = Length of the rectangular paper sheet - (2 × 0.5) = L - 1.
- Width of the box = Width of the rectangular paper sheet - (2 × 0.5) = W - 1.
- The height of the box would be the height of the cylindrical paper sheet, which is "W".
5. Calculate the volume of the cuboidal box:
- The volume of a cuboid is given by V = Length × Width × Height.
- Substituting the values from step 4, V = (L - 1) × (W - 1) × W.
Now, you can substitute the given values into these equations to find the volume of the box.