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A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 4 cm and diameter of the base is 8 cm. Determine the volume of the toy. If the cube circumscribes the toy, then find the difference of the volumes of the cube and the toy. Also, find the total surface area of the toy.

Tutor

surface area=171.3cm² difference in volume=311cm³

Math magician

height of cone = 4cm ,radius of cone = 8/2 =4cm .. now volume of toy = volume of cone + volume of hemis phere .so total volume = 2/3 π r3 + 1/3 π r2 h = π r2 ( 2/3 r + 1/3 h ) = 22/7 × 4×4 (2/3 × 4 +1/3×4) = 22/7 × 16 (8/3 +4/3) = 22/7× 16... read more

height of cone = 4cm  ,radius of cone = 8/2 =4cm .. now volume of toy  =  volume of cone + volume of hemis phere  .so  total volume  =  2/3 π r3  + 1/3 π rh  =  π r2 ( 2/3  r +  1/3 h )  = 22/7 × 4×4  (2/3 × 4 +1/3×4)    = 22/7 × 16 (8/3 +4/3) = 22/7× 16 ×4 =  22/7 ×64  cube cm .  Curbed surface area of cone =                                 π r l =π 4 √ (h2   +r2 )    =π ×4 √(16+16) = π4√ 32    =22/7 × 16√2    surface area of toy =2π r2 + πrl . = 22/7 × 2× 16  + 22/7  ×16√2    =22/7  ( 32 + 16√2)   = 3.14× 54.56= 171.31 cm square' answer                                                  Difference of volume of cube and toy = 83 - 22/7 × 64 = 512 - 201 = 311 cube cm answer

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