math
posted by Anonymous .
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.

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 
Thank you
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