Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A conical cavity is drilled in a circular cylinder of 15 cm height and 16 cm base diameter. The height and base diameter of the cone are the same as those of the cylinder. Determine the total surface area of the remaining solid.
(a)$215 \pi \mathrm{cm}^{2}$
(b)$376 \pi \mathrm{cm}^{2}$
(c)$440 \pi \mathrm{cm}^{2}$
(d)$542 \pi \mathrm{cm}^{2}$
Answer
Answer (as printed): C
Explanation
Total surface area of the remaining solid = Curved surface area of the cylinder + Area of the base of the cylinder + Curved surface area of the cone $=2 \pi r h+\pi r^{2}+\pi r \sqrt{r^{2}+h^{2}}$ $=2 \pi \times 8 \times 15+\pi \times 8^{2}+\pi \times 8 \times \sqrt{8^{2}+(15)^{2}}$ $=240 \pi+64 \pi+136 \pi=440 \pi \mathrm{sq} . \mathrm{cm}$.
Explanation as extracted from the printed page; notation may be imperfect.