Question : From a solid right circular cylinder of length 4 cm and diameter 6 cm, a conical cavity of the same height and base is hollowed out. The whole surface of the remaining solid (in square cm) is:
Option 1: 48$\pi$
Option 2: 15$\pi$
Option 3: 63$\pi$
Option 4: 24$\pi$
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Correct Answer: 48$\pi$
Solution : Given: Diameter = 6 cm So, radius, $r$ = $\frac{6}{2}$ = 3 cm Height, $h$ = 4 cm $\therefore$ Curved surface area of the cylinder $=2\pi rh=2\pi×3×4=24\pi$ Now, slant height, $l$ = $\sqrt{r^2+h^2}$ = $\sqrt{3^2+4^2}$ = $5$ So, the curved surface area of the cone $=\pi rl=\pi×3×5=15\pi$ Area of the circle on the top $=\pi r^2=\pi×3^2=9\pi$ Required whole surface area = curved surface area of cylinder + curved surface area of cone + area of the circle = $24\pi+15\pi+9\pi$ = $48\pi$ Hence, the correct answer is 48$\pi$.
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