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Q.

A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 19 cm and the diameter of the cylinder is 7cm. Find the volume of the solid.

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a

582.67 cm 3  

b

758.67 cm 3    

c

641.67 cm 3  

d

658.67 cm 3  

answer is A.

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Detailed Solution

Given, the diameter of the cylinder is 7cm.
As the radius of the hemisphere = radius of the cylinder = 3.5 cm.
So, the radius of the hemisphere = 3.5cm.
The figure is shown below,
Question ImageIt is given that the total height of the solid is 19 cm.
So, the height(h) of the cylinder,
h=19−7  
h=12 cm
Let the volume of the hemisphere be V1 and the volume of the cylinder be V2.
So, volume of the two hemispheres,
V 1 =2× 2 3 π r 3   V 1 = 4 3 × 22 7 × (3.5) 3   V 1 =179.67   cm 3   The volume of the cylinder is,
V 2 =π r 2 h   V 2 = 22 7 × (3.5) 2 ×12   V 2 =462   cm 3   Therefore, the volume(V) of the solid, V= V 1 + V 2   .
⇒179.67+462   ⇒641.67   cm 3  
Hence, the volume of the solid is 641.67 cm 3   .
Therefore, the correct option is 1.
 
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