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A glass in the form of a frustum of a cone is represented by the diagram below. The glass contains water to height of 9 cm. The bottom of the glass is circle of radius 2cm while the surface of the water is a circle of radius 6 cm.

(a) Calculate the volume of the water in the glass.
(b) When spherical marble is submerged into the water in the glass, the water level rises by 1 cm. calculate:
(i) The volume of the marble
(ii) The radius of the marble.

• math -

using similar triangles, the height of the cone that was cut off to form the glass is 4.5cm. So, the volume of the part cut off is

1/3 pi (2^2)(4.5) = 6pi cm^3

(a) v = 1/3 pi (6^2)(13.5) - 6pi = 156pi
(b)
with marble submerged, volume is increased by (14.5/13.5)^3 = 1.24, or
(i) 37.3pi = 117cm^3
(ii) r = 3cm

• math -

Thank you

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