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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

Let’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) = πr2 + 2πrh + πrl

V1 = π(5)2 + 2π(5)(12) + π(5)(13)

V1 = 210 π cm2

And, the volume of the remaining portion of the circular cylinder = Volume of the cylinder – Volume of the 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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