Question

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

Answer 1

Answer :- The Whole surface area of the remaining cylinder is S = 210π cm²and the volume of the remaining portion of the cylindrical part is  V = 200 π cm³

Solution:-

Height of the circular Cylinder & cone , h = 12 cm

Base radius of the circular Cylinder & cone , r = 5 cm

Slant height of the cone , l = √r² + h²

l = √5²  + 12²  

l = 25 + 144

l = √169

l = 13 cm

Now,

Whole surface area of the remaining portion in the circular cylinder ,S  = Area of base of the cylinder + curved surface area of cylinder + curved surface area of cone  

S = πr² + 2πrh + πrl

S = π(r² + 2rh + rl)

S = π [(5)²  + 2( 5)(12)  + (5 )(13 )]

S = π[25 + 120 + 65]

S = π× 210

S = 210 π cm²

Hence, the Whole surface area of the remaining cylinder is 210π cm².

Volume of the remaining portion of the circular cylinder = Volume of the cylinder – Volume of the cone

V = ( πr²h – ⅓ × πr²h)

V = ⅔ × πr²h

V = ⅔ × π × 5² × 12  = 2 × π × 25 × 4  

V = 200 π cm²

Hence, the Whole surface area of the remaining cylinder is 210π cm²and the volume of the remaining portion of the cylindrical part is  V = 200 π cm³

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