From a solid cylinder whose height is 2.4 cm and diameter is 1.4 cm, a conical cavity of the same height and the same diameter is carved out. The total surface area of the remaining solid is: (Use \(\pi=\frac{22}{7}\))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 17.6 cm2
Once the cone is carved out of one end, the remaining solid is bounded by three surfaces: the curved surface of the cylinder, its one remaining circular end, and the curved surface of the conical hollow (the other end is now the mouth of the cavity).
The measurements (radius = half the diameter):
\(r=0.7\) cm, \(h=2.4\) cm
Slant height of the cone: \(l=\sqrt{2.4^2+0.7^2}=\sqrt{6.25}=2.5\) cm
Adding the three surfaces:
Total surface area \(=2\pi rh+\pi r^2+\pi rl=\pi r(2h+r+l)\)
\(\displaystyle=\frac{22}{7}\times0.7\times(4.8+0.7+2.5)\)
\(=2.2\times8=17.6\) cm2