A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #42 # and the height of the cylinder is #1 #. If the volume of the solid is #495 pi#, what is the area of the base of the cylinder?

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Answer 1 · 2017-01-22T17:05:27

#33pi#.

Let #r# be the radius of the Cone, so, that of the Cylinder is also #r#.

#"Now, the Volume v_1 of the cone="1/3pir^2"(height)"=1/3pir^2(42)#,

and, the Vvolume #v_2" of the cylinder="pir^2"(height)"=pir^2(1).#

#:." Total Volume of the solid="v_1+v_2=14pir^2+pir^2=15pir^2#

As this Volume is #495pi," we have, "15pir^2=495pi#

#:."The Area of the base of the cylinder="pir^2=(495pi)/15=33pi#.