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Question -

A conical hole is drilled in a circular cylinder of height 12 cm and base radius 5 cm. The height and base radius of the cone are also the same. Find the whole surface and volume of the remaining Cylinder.



Answer -


Given,

Height of the circularCylinder (h1) = 12 cm

Base radius of thecircular Cylinder (r) = 5 cm

Height of the conicalhole = Height of the circular cylinder, i.e., h= h=12 cm

And, Base radius ofthe conical hole = Base radius of the circular Cylinder = 5 cm

Let’s consider, L asthe slant height of the conical hole.

Then, we know that

Now,

The total surface areaof the remaining portion in the circular cylinder (V1) = πr+2πrh + πrl

V=π(5) + 2π(5)(12) + π(5)(13)

V=210 π cm2     

And, the volume of theremaining portion of the circular cylinder = Volume of the cylinder – Volume ofthe conical hole

V = πr2h– 1/3 × 22/7 × r2 × h

V = π(5)2(12)– 1/3 × 22/7 × 52 × 12

V = 200 π cm2

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