Conical hole is drilled in a cylindrical of height 12cm and base radius 5 cm
Answers
Answer:
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
Step-by-step explanation:
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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