Mathematics
The adjoining figure shows a model of a solid consisting of a cylinder surmounted by a hemisphere at one end. If the model is drawn to a scale of 1 : 200, find
(i) the total surface area of the solid in π m2.
(ii) the volume of the solid in π litres.
Mensuration
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Answer
(i) In the given figure,
Height of cylindrical portion (H) = 8 cm.
Radius (r) = 3 cm.
Scale = 1 : 200
∴ k = 200.
Total surface area (S) = Surface area of hemisphere + Curved surface area of cylinder = 2πr2 + 2πrH
∴ Surface area of solid = 66π × k2 = 66π × (200)2
= 66π × 40000 cm2
= m2
= 264π m2.
Hence, the surface area of solid = 264π m2.
(ii) Volume (V) = Volume of hemisphere + Volume of cylinder =
Putting values we get,
∴ Volume of solid = 90π × k3 = 90π × (200)3
= 90π × 8000000 = 72000000π cm3
=
= 720π m3.
1 m3 = 1000 litres.
∴ Volume of solid = 720π × 1000 = 720000π litres.
Hence, the volume of solid = 720000π litres.
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