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A solid consists of a right circular cone of height 12 cm surmounted on a right circular cylinder of the same height and radius 5 cm. Determine the total area and volume of a solid.

jhayzen1728  Aug 11, 2018
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The cone will have 1/3 of the volume of the cylinder

 

The  volume of the cylinder is   pi * radius^2 * height  =  pi * (5)^2 * 12  =  pi * 25 * 12 = 300 pi cm^3

So the volume of the cone is  300pi / 3  = 100 pi cm^3

 

So....the volume of the solid is  [ 300 + 100] pi cm^3  = 400pi cm^3

 

The lateral  area of the cylinder   is  2pi * radius * height  = 2pi * 5 * 12  =  120 pi cm^2

The area of the bottom of the cylinder  is  pi * radius^2  = pi * 5^2  = 25 pi cm^2

 

The slant height of the cone is √ [ height^2 + radius^2 ]= √ [12^2 + 5^2]  =√169  = 13 cm

So....the lateral area of the cone is  pi * radius * slant height  = pi * 5 * 13  = 65 pi cm^2

So...the total area  of the  solid is  [ 120 + 25 + 65] pi  = 210 pi cm^2

 

 

 

cool cool cool

CPhill  Aug 11, 2018

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