We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
273
3
avatar+10 

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.

 Aug 11, 2018
 #2
avatar+100519 
+2

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

 Aug 11, 2018

13 Online Users