Maths-
General
Easy

Question

A Toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other end. The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radii of hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy if the height of the conical part is 12 cm

hintHint:

Volume of cylinder equals pi r squared h

The correct answer is: 770cm


    Explanation:
    • We have given A Toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other end. The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radii of hemispherical and conical parts are the same as that of the cylindrical part
    • We have to find the surface area of the toy if the height of the conical part is 12 cm.
    Step 1 of 1:
    We have
    Radius of base of the cylinder 5cm
    Radius of base of the cone 5cm
    Height of hemisphere = its radius = 5cm
    Then
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 5 plus 13 plus h equals 30 end cell row cell h equals 12 cm end cell end table
    Total area of the toy = CSA of cone + CSA of cylinder + CSA of Hemisphere
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals 2 pi r squared plus 2 pi r h plus pi r open parentheses square root of r squared plus h squared end root close parentheses end cell row cell equals 2 pi cross times 5 squared plus 2 pi cross times 5 cross times 13 plus pi 5 open parentheses square root of 5 squared plus 12 squared end root close parentheses end cell end table
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals 50 pi plus 130 pi plus 65 pi end cell row cell equals 245 pi end cell row cell equals 770 cm squared end cell end table

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