Q) A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weights, a conical hole is drilled in the cylinder. The conical hole has a radius of cm and its depth cm. Calculate the ratio of the volume of metal left in the cylinder to the volume of metal taken out in conical shape.

Ans:

Step 1: ∵ Volume of the cylinder = π  r ² h

For cylinder, radius = 3 cm and height = 5 cm   (given)

∴ Cylinder’s volume = π × (3)² × 5 = π × 9 × 5 = 45 π cm³

Step 2: ∵ Volume of the cone = π r ² h

For conical hole, radius =  cm and height = cm   (given)

∴ Conical hole’s volume =

=  

= π cm³

Step 3: ∵ Volume of remaining body  = Cylinder volume – Conical hole’s volume

= 45 π – π

= π cm³

Step 4: ∵ Ratio of volumes of metal left to metal taken out:

= Volume of remaining body : Volume of conical hole

=

= 133 : 2 = 66.5 : 1

The required ratio of metal’s volume is 66.5 : 1

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