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A wooden toy rocket is made of a cone mounted on a cylinder, as shown. The total height is $26\,\mathrm{cm}$, the conical part has height $6\,\mathrm{cm}$, the cone's base diameter is $5\,\mathrm{cm}$, and the cylinder's base diameter is $3\,\mathrm{cm}$. If the conical portion is painted orange, which area should be painted orange? 
AOnly the curved surface area of the cone
BCSA of cone $+$ full base area of cone
CCSA of cone $+$ base area of cone $-$ base area of cylinder
DCSA of cone $-$ base area of cylinder
Answer & Solution
Correct answer: C. CSA of cone $+$ base area of cone $-$ base area of cylinder
Because the cone sits on the cylinder but has a larger base, the entire circular base of the cone is not hidden. Only the portion directly covering the cylinder is not exposed. Hence the orange-painted part is the cone's curved surface plus the exposed ring on its base, i.e. $\pi rl+\pi r^2-\pi {r'}^2$.
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