From a solid cylinder whose height is 2.4cm and diameter 1.4cm, a conical cavity of the same height and the same diameter is hollowed out. The total surface area of the remaining solid to the nearest

c
m
2

is ____.

Question

From a solid cylinder whose height is 2.4cm and diameter 1.4cm, a conical cavity of the same height and the same diameter is hollowed out. The total surface area of the remaining solid to the nearest

c
    m
    2

is ____.

Accepted Answer

According to the given information, a height of 2.4 cm of a solid cylinder with a diameter of 1.4 cm, where the same conical cavity is hollowed out at the same height and diameterSo the dimensions we know areHeight of full cylinder (v) = 2.4 cmDiameter of solid cylinder (d) = 1.4 cmTherefore, the radius of the solid cylinder (r) = 0.7 cmAs we know, the formula of the total surface of the remaining solid is equal to the curved surface of the cylinder + the area of ​​​​the base of the cylinder + the curved surface of the coneNow we know that the curved surface of the cylinder =

2πrh
  Area of the base of the cylinder

π
    r
    2

and Curved surface area of the cone

πrl
  .Where

l
  slant height which is given as

l=

r
      2
     
     +
      h
      2

Therefore, Total surface area of the remaining solid =

2πrh+π
    r
    2
   
   +πr

r
      2
     
     +
      h
      2

Now substituting the values in the above formula, we get

2×
      
       22
      7
     
     ×0.7×2.4+
      
       22
      7
     
     ×
      (0.7)
      2
     
     ×

(2.4)
        2
       
       +
        
         (0.7)
        2

⇒10.56+1.54+5.5c
      m
      2

⇒17.6c
      m
      2

So, Total surface area of the remaining solid is equal to

17.6c
    m
    2

.

From a solid cylinder whose height is 2.4cm and diameter 1.4cm, a conical cavity of the same height and the same diameter is hollowed out. The total surface area of the remaining solid to the nearest $c m 2$ is ____.

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From a solid cylinder whose height is 2.4cm and diameter 1.4cm, a conical cavity of the same height and the same diameter is hollowed out. The total surface area of the remaining solid to the nearest c m 2 is ____.