Question

A solid iron toy consisting of a right circular cone of lateral height 5cm. and the base diameter is 8cm.which is surmounted on hemisphere is placed upright in a right circular cylinder full of water such that it touches the bottom.Find the volume of water left in the cylinder if the radius of the cylinder is 4cm and height is equal to the iron toy. solution for this problem

Answer 1

Water left in cylinder = 33.52 cm³

Step-by-step explanation:

radius = diameter / 2 = 8/2 = 4 cm

height of cone = 5 cm

volume of cone =  πr²h/3

volume of surmounted hemisphere=    2πr³/3

Volume of toy  = volume of cone +  volume of surmounted hemisphere

= πr²h/3 +  2πr³/3

= π (r²h/3 +  2r³/3)

= π ( 1/3*4*4*5 + 128/3)

= π ( 80/3 + 128/3)

= π 208/3  sq. cm

Water left in cylinder = volume of cylinder - volume of toy

=  πr²h - volume of toy

= π*4*4*5 - π 208/3

= π (80 - 208/3)

=  22/7 * (240-208)/3

= 22 * 32 / 21

= 33.52 cm³