maths-urgently needed

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

  1. 👍 2
  2. 👎 1
  3. 👁 1,776
  1. 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

    1. 👍 0
    2. 👎 3
  2. 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!
    Jay Bankoti

    1. 👍 7
    2. 👎 1
  3. Volume of a cylinder = pi * r^2 * h

    As per the question,
    pi * r^2 * h = 48.125
    r^2 * h = 48125/10000 * 7/22
    r^2 * h = (49 * 5) / 16
    r^2 * h = (7^2 * 5) / 4^2
    r^2 = (7^2 * 5) / 4^2 * h

    To make r^2 perfectly get converted into a value with a power of 1, we must cancel out the extra 5 that is making the RHS unable to be completely squared. We can so this by the extra 'h' variable that we have. So the height of the cylinder or the breadth of the paper is 5 cm.

    r^2 = 7^2 / 4^2
    r = 7/4

    Since the length of the paper would be 2 * pi * r
    l = 2 * 22/7 * 7/ 4 = 11 cm

    If we draw 4 o.4 squares at the 4 corners of the page, we may observe the fact that when we fold the remains inward, it forms a cuboid without a top, with a hight of 0.5 cm. The breadth of the page is 5cm, but because 0.5cm squares are at both ends, 1 cm is reduced to calculate the real breadth of the cuboid. In the same way, the length of the page will also be reduced by 1 to calculate the length of the cuboid.

    So (for the cuboid),
    length = 11-1 = 10cm
    breadth = 5-1 = 4cm
    height = 0.5cm
    Therefore the volume of the cuboid (box) = 10 * 4 * 0.5 = 20cm^3

    1. 👍 1
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Chemistry

    The density of pure silver is 10.5 g/cm3 at 20 °C. If 5.25 g of pure silver pellets is added to a graduated cylinder containing 11.2 mL of water, to what volume level will the water in the cylinder rise?

  2. maths

    A rectangular sheet of paper 30 cm X 18cm can be transformed into a right circular cylinder in two ways - by rolling the paper along its length or by rolling it along its breadth . Find the ratio of the volume of two cylinders

  3. Science

    What is the density of a book whose mass is 1,800 g and whose volume is 300 cm3? *My Answer*You want to identify the numbers first, density = mass ÷ volume. Which would give you, 1800g ÷ 300 cm³ = 6 g/cm³. *Cant Figure Out

  4. Chemistry

    Iron has density 7.87 g/cm3. If 52.3 g of iron is added to 74.5 mL of water in a graduated cylinder, to what volume reading will the water level in the cylinder rise? mL

  1. chemistry

    Block A of an unknown metal has a volume of 125 cm3. Block B of a different metal has a volume of 145 cm3. If block A has a greater mass than block B, what can be said of the relative densities of the two metals? (Assume that both

  2. algebera

    1) Identify the solid form by the given net. :Triangular Prism :Triangular Pyramid*** :Cone :Triangle 2) Name the solid according to it's description: The figure has two bases that are parallel congruent circles. :Cylinder***

  3. geometry

    the volume of a cube is 125 cm3. What is the length of each side?

  4. Chemistry

    the mass of cylinder one is 1.35 times the mass of cylinder two, and the volume of cylinder one is 0.792 times the volume of cylinder two. If the density of cylinder one is 2.70 g/cm3 what is the density of cylinder two? THIS

  1. math

    which of the following expressions shows the equation to use in the finding the dimensions of a cube N by N by N with a volume 125 1) n3=125 2) n2=125 3) 3n=125 4) n=125/3 5) not enought info given need help with this problem!!

  2. math

    A solid sphere of radius Xcm is placed in a cylinder of radius 2Xcm and height 2Xcm. The cylinder is then filled with water to the brim and the solid gently withdrawn. Find d volume of d water in d cylinder in cm3

  3. math

    which of the following expressions shows the equation to use in finding the dimensions of a cube n by n by n with a volume of 125? 1]n3=125 2]n2=125 3]3n=125 4]n=125-3 5] not enough information is given.

  4. Geometry

    32. What is the maximum volume of a square pyramid that can fit inside a cube with a side length of 18cm? 5,832 cm3 2,916 cm3 1,944 cm3 972 cm3

You can view more similar questions or ask a new question.