maths

posted by .

A Toy is in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of the hemisphere .If the radius of base of the cone is 21 cm and its volume is 2/3 of the volume of hemisphere calculate the height of cine and surface area of the toy.

  • maths -

    The missing part is the height of the cone, but it is 2/3 the volume of the hemisphere (semi-sphere).

    volume of hemisphere = (1/2 (4/3)π (21^3) = 6174π
    but the volume of the cone is 2/3 of that or 4116π

    vol of cone = (1/3)π r^2 h
    4116π = (1/3)π(21^2)h
    12348 = 441h
    h = 28

    Now use your formulas for surface area of a sphere, take half of that , and use your formula for the surface area of a cone with radius 21 and height 28
    Make sure NOT to include the circular base joining them when finding surface area

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. AP Calculus..again

    A balloon is composed of a right circular cone joined at its base to a hemisphere. The diameter of the base is equal to the height of the cone. If the balloon is inflated, at what rate is the volume, V, changing with respect to the …
  2. Math 214

    How do you find the volume of a right circular cone with a hemisphere?
  3. geometry

    A cone is topped with a hemisphere. Calculate the total surface area if the radius of the cone and hemisphere is 10 cm and the height of the cone is 24 cm.
  4. Calculus

    Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the center of the base of the larger cone, and its base is parallel to the base of the larger cone. If you choose the upside-down cone to have …
  5. math

    Two right circular cone, one upside down in the other. The two bases are parallel. The vertex of the smaller cone lies at the center of the larger cone’s base. The larger cone’s height and base radius are 12 and 16 ft, respectively. …
  6. maths-surface area

    A solid is in the form of cone mounted on a hemisphere in such a way that the centre of the base of the cone just coincide with the centre of the base of the hemisphere. Slant height of the cone is L and radius of the base of the cone …
  7. Calculus: Optimization

    I have no idea how to approach this problem, if someone knows just how to relate h, r with H,R, that would be extremely helpful and I can workout the rest! Thank you in advance. Given a right circular cone, you put an upside-down cone …
  8. Math

    a cone and a hemisphere share the base that is a semicirclee with radius 3 and the cone is inscribed inside the hemisphere. find the volume of the region inside the hemisphere
  9. math

    A right circular cone stands on a hemisphere. The base radius of the cone is equal to the radius of the hemisphere. If the base radius of the cone is 10 centimeters and its height is 15 centimeters,calculate the total volume of the …
  10. Math

    Please Help A body consists of a solid hemisphere of radius r joined to a right circular cone of base radius r and perpendicular height h. The plane surfaces of the cone and hemisphere coincide and both solids are made of the same …

More Similar Questions