math

posted by .

Dana takes a sheet of paper, cuts a 120-degree circular sector from it, then rolls it up
and tapes the straight edges together to form a cone. Given that the sector radius is 12
cm, find the height and volume of this paper cone.

  • math -

    The circumference of the whole circle from which you cut the sector is 2π(12) = 24π cm

    so using ratios to find the circumference of the sector:
    120/360 = x/24π
    x = 8π

    That becomes the circumference of the base of the cone
    for its radius r :
    2πr = 8π
    r = 4 cm
    The radius of the original sector becomes the slant side of the cone
    so h^2 + 4^2 = 12^2
    h = √128 = 8√2

    vol = πr^2h/3 = π(4)^2(8√2)/3 = (128π√2)/3 cm^3 or appr. 189.563

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. geometry

    11. Infinitely many different sectors can be cut from a circular piece of paper with a 12-cm radius, and any such sector can be fashioned into a paper cone with a 12-cm slant height. (a) Show that the volume of the cone produced by …
  2. Geometry

    Infinitely many different sectors can be cut from a circular piece of paper with a 12-cm radius, and any such sector can be fashioned into a paper cone with a 12-cm slant height. (a) Show that the volume of the cone produced by the …
  3. PreCalculus

    Cone Problem Beginning with a circular piece of paper with a 4- inch radius, as shown in (a), cut out a sector with an arc of length x. Join the two radial edges of the remaining portion of the paper to form a cone with radius r and …
  4. Math

    Cone Problem Beginning with a circular piece of paper with a 4- inch radius, as shown in (a), cut out a sector with an arc of length x. Join the two radial edges of the remaining portion of the paper to form a cone with radius r and …
  5. Math

    I already posted this, but wanted to say that I have the answers and it is 1.68 is less than or equal to x is less than or equal to 9.10 Cone Problem Beginning with a circular piece of paper with a 4- inch radius, as shown in (a), …
  6. CALCULUS

    A cone shaped paper drinking cup is to be made from a circular piece of paper of radius 3 inches by cutting out a sector of the circle and gluing the straight edges together. Find the angle of the cut that gives the cup with the largest …
  7. Math

    A cone is constructed by cutting a sector from a circular sheet of metal with radius 20cm. The cut sheet is then folded up and welded. Find the radius and height of the cone with the maximum volume that can be formed in this way.
  8. calculus

    A paper cone is to be formed by starting with a disk of radius 9cm, cutting out a circular sector, and gluing the new edges together. The size of the circular sector is chosen to maximize the volume of the resulting cone. How tall …
  9. calculus

    A paper cone is to be formed by starting with a disk of radius 9cm, cutting out a circular sector, and gluing the new edges together. The size of the circular sector is chosen to maximize the volume of the resulting cone. How tall …
  10. calculus

    A paper cone is to be formed by starting with a disk of radius 9cm, cutting out a circular sector, and gluing the new edges together. The size of the circular sector is chosen to maximize the volume of the resulting cone. How tall …

More Similar Questions