Problem from RS Aggarwal book page number 289, exercise 17A, chapter volume and surface area of solid.

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# A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical part are 5 cm and 13 cm, respectively. The radii of the hemispherical and the conical parts are the same as that of the cylindrical part. Find the surface area of the toy, if the total height of the toy is 30 cm.

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Given data

Total height = 30cm

height of cylinder = 13cm

height of cone = 30-18 (radius of hemisphere=height [ given ])

∴height of cone= 12cm

Curved surface area of hemisphere = 2*πr²

= 2*[22/7]*5²

= 157.14 cm²

Curved surface area of cylinder = 2*πrl

= 2*[22/7]*5*13

= 408.571 cm²

Curved surface area of cone = πrl

= [22/7]*5*13

=204.28

Adding all Curved surface area as we get = 408.57 + 204.2 + 157.14

= 769.99 cm²

∴ Total surface area of the toy is 769.99 cm²