A conical cavity is drilled in a solid right circular cylinder of 6 cm height and 16 cm base diameter. The height and the base diameter of the cone are the same as those of the cylinder. Determine total surface area off the remaining solid?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 240π cm2.
Given:
A conical cavity is drilled in a solid right circular cylinder of 6 cm height and 16 cm base diameter.
Formula used:
Curved surface area of cone = πrl ---- (1)
Curved surface area of cylinder = 2πrh ---- (2)
Calculations:
Using equation (1) and (2),
Slant height can be calculated by using Pythagoras theorem
⇒ (Slant height)2 = (radius)2 + (height)2
⇒ 82 + 62 = 100 = 10
Now, according to the question,
Required surface area = curved surface area of cylinder + curved surface area of cone + Area of circular base
⇒ 2πrh + πrl + πr2
⇒ π(2rh + rl + r2)
⇒ π(96 + 80 + 64) = 240π cm2