A) \[15\pi \,sq\,cm\]
B) \[22\pi \,sq\,cm\]
C) \[33\pi \,sq\,cm\]
D) \[48\pi \,sq\,cm\]
E) None of these
Correct Answer: D
Solution :
Explanation Option [d] is correct. The resulting solid look like as follows: Here the unshaded portion is a hollow. Thus, total surface of remaining solid will be the bottom circle of cylindrical portion, curved surface of cylinder and the inner curved surface area of cone. Now, surface area of bottom of circle = \[\pi {{r}^{2}}=9\pi sq\,\,cm\] Curved surface area of cylinder = \[2\pi rh=2\pi \left( 3 \right)\left( 4 \right)=24\pi \,\,sq\,\,cm\] Slant height of cone \[\ell =\sqrt{{{r}^{2}}+{{h}^{2}}}=\sqrt{{{3}^{2}}+{{4}^{2}}}=5\,cm\] Curved surface area of cone = \[\pi r\ell =\pi \left( 3 \right)\left( 5 \right)=15\pi \,sq\,cm\] Total surface area of resulting solid = \[9\pi +24\pi +15\pi =48\pi \,sq\,cm\,\]You need to login to perform this action.
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