Q) Both the ends of a metallic solid cylinder are semi-spherical. Its total height is 19 cm and diameter of the cylinder is 7 cm. Find the weight of the solid if weight of 1 cm³ of the metal is 4.5 g.

Ans:

Step 1: Let’s make  diagram for our better understanding of the question:

Step 2: Here, we can see that the spherical ends are joined with the cylinder and have similar width.

∵ Diameter of the cylinder = 7 cm

∴ Diameter of the spherical ends = 7 cm

∴ Radius of the spherical ends = cm

Step 3: Given that the total height of the object = 19 cm

Height if the cylindrical part = Total height – 2 x radius of a hemispherical end

(There object has 2 spherical end, one each on left and right side)

= total height – diameter of a hemispherical end

= 19 – 7 = 12 cm

Step 4: Next, the Volume of the object = Volume of the cylinder + 2 x Volume of the hemispherical ends

= π r ² h + 2 x π r ³  = π r ² (h + r)

=

=

=  = cm³

Step 5: Given that the weight of 1 cm³ metal is = 4.5 g

∴ Weight of    cm³ metal will be =  x 4.5

=  = 3850 x   = 3850 x 

= 1925 x   =

= 2887.50 gm = 2.8875 kg

Therefore, the weight of the given solid object is 2.8875 kg.

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