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# 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.

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Very important question of mensuration including
very important concept of it.need solution!
Rd sharma class 10 maths exercise-16.2 mensuration.

we have to find the whole surface and volume of the remaining Cylinder.
From 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.

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1. Given,

Height of the circular Cylinder (h1) = 12 cm

Base radius of the circular Cylinder (r) = 5 cm

Height of the conical hole = Height of the circular cylinder, i.e., h1 = h2 = 12 cm

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

Letâ€™s consider, L as the slant height of the conical hole.

Then, we know that

R D Sharma Solutions For Class 10 Maths Chapter 16 Surface Areas And Volumes ex 16.2 – 7

Now,

The total surface area of the remaining portion in the circular cylinder (V1) = Ï€r2 + 2Ï€rh + Ï€rl

V1 = Ï€(5)2 + 2Ï€(5)(12) + Ï€(5)(13)

V1 = 210 Ï€ cm2

And, the volume of the remaining portion of the circular cylinder = Volume of the cylinder â€“ Volume of the conical hole

V = Ï€r2h â€“ 1/3 Ã— 22/7 Ã— r2 Ã— h

V = Ï€(5)2(12) â€“ 1/3 Ã— 22/7 Ã— 52 Ã— 12

V = 200 Ï€ cm2

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