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A drinking glass is shaped like a cylinder with a height of 12 cm and a radius of 4 cm. Maeva adds 25 spherical pieces of ice to the glass. The pieces of ice each have a diameter of 3 cm.

How many cubic centimeters of water can Maeva add to fill the glass to the rim?
Use 3.14 to approximate pi and express your answer in hundredths.



Answer :

jzakoian
The volume of the cylinder is L*[tex] \pi r ^{2} [/tex]
Which is 12 * 3.14 * 4[tex] ^{2} [/tex]
=602.88 cubic cm

Each piece of ice's volume is defined as 4/3*[tex] \pi *r ^{3} [/tex] cubic cm (volume of a sphere). With r=3/2 (since 3 cm is the diameter)
=4/3 * 3.14 * (3/2)[tex] ^{3} [/tex]
=14.13 cubic cm

25 of those cumulate a total volume of 25 * 14.13 = 353.25 cm[tex] ^{3} [/tex]
Which means that the free space for water is 602.88-353.25=249.63 cubic cm

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