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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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582.67 cm

3

758.67 cm

3

641.67 cm

3

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 Image

It 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 × 23 π r 3

V 1 = 43 × 227 × (3.5) 3

V 1 = 179.67

3

The volume of the cylinder is,

V 2 = π r 2 h

V 2 = 227 × (3.5) 2 × 12

V 2 = 462

3

Therefore, the volume(V) of the solid,

V = V 1 + V 2

⇒ 179.67 + 462

⇒ 641.67

3

Hence, the volume of the solid is 641.67 cm

3

.
Therefore, the correct option is 1.

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