A cone of maximum size is carved from a square prism of base edge 30cm and height 20cm
a) What is the base radius of the cone?
b) What is the slant height of the cone?
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Given: Side of the cube =14 cm
Volume of the cube =(14)
3
=2744 cm
3
The biggest cone that can be carved out will be having the height of 14 cm and diameter will be 14 cm
Hence the radius =7 cm
Volume of biggest cone that can be carved =
3
1
πr
2
h
=
3
1
×
7
22
×7×7×14
=
3
1
×22×7×14
=
3
2156
=718.66 cm
3
The volume of remaining solid =2744−718.66
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