Posted by Anonymous on Wednesday, January 16, 2013 at 12:24pm.
The volume of a cylinder is 48.125 cm3, which is formed by rolling a rectangular paper sheet along the length of the paper. If cuboidal box (without any lid i.e., open at the top) is made from the same sheet of paper by cutting out the square of side 0.5 cm from each of the four corners of the paper sheet, then what is the volume of this box
- maths-urgently needed - Reiny, Wednesday, January 16, 2013 at 4:43pm
let the width of the sheet of paper be x
let its length be y
so the cylinder made from it would have a height of y
the width would be its circumference
2πr = x
r = x/(2π)
volume = πr^2 h = π(x^2/(4π^2) y = x^2 y/(4π)
48.125 = x^2 y/(4π)
192.5π = x^2y
y = 192.5/x^2
now to the box:
length = (y-1)
width = (x-1)
height = .5
volume = .5(x-1)(y-1) = .5(x-1)(192.5/x^2 - 1)
= (1/2)(192.5/x - x - 192.5/x^2 + 1)
getting nowhere .....
not enough information
in the first part, there is no unique solution for x and y
which would change the shape of the sheet of paper, which would change the volume of the resulting box
- maths-urgently needed - Jay Bankoti, Sunday, November 24, 2013 at 11:01am
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 Reiny!
Answer This Question
More Related Questions
- maths - what is the volume of box if volume of cylinder is 48.125 cubic cm, ...
- maths --plse help me.. - THE VOLUME OF A CYLINDER IS 48.125cm cube , WHICH IS ...
- maths - A rectangular sheet of paper 30 cm X 18cm can be transformed into a ...
- volume - hi, um im not sure how to do this.So can you please help me? coral ...
- Calc - A gift box measures 6 in. along each edge You cut a rectangular sheet of ...
- maths - a paper box without a lid is 25 cm long. 16 cm wide and 5 cm deep . how ...
- Math - You want to create a box without a top from an 8.5 in by 11 in sheet of ...
- Math - From an 8 inch by 10 inch rectangular sheet of paper, squares of equal ...
- math - Alex must wrap two boxes. Both boxes are right rectangular prisms. The ...
- ALGEBRA - DAmon you equaled them to zero that is not rightt An open-topped box ...