The correct answer is: [A]: " 1944 pi cm sq" .
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The exact surface area of the given "right cylinder" is: " 1,944 π cm² " .
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Explanation:
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The formula for the "surface area, S.A." of a right cone is:
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→ S. A. = π r [ r + √(h² + r²) ]
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in which: "S. A." is the "surface area" (in units of "cm² " ; in our case) ;
→ for which we shall solve;
π = π ; (Note, we are asked to solve for the EXACT surface area of the given "right cone" ; so we shall solve in terms of "π" ; & we note that the answer choices provided are all "in terms of π" ;
" r = "radius" of the [circular base] = diameter / 2 ;
= 54 cm / 2 = 27 cm ;
" h = perpendicular height = 36 cm " ;
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→ Plug in our known values into the formula/equation ;
for the "surface area, S.A." of a right cone to solve:
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→ S. A. = π r [ r + √(h² + r²) ] ;
→ S.A. = π * (27 cm) * [ 27 cm + √[ (36 cm)² + (27 cm)² ] ;
= π * (27 cm) * [ 27 cm + √[ (36² * cm²) + (27² cm²) ] ;
= π * (27 cm) * [ 27 cm + √[ (1296 cm²) + (729 cm²) ] ;
= π * (27 cm) * [ 27 cm + √ [ (1296 + 729) cm² ] ;
= π * (27 cm) * [ 27 cm + √ [ (1296 + 729) cm² ] ;
= π * (27 cm) * [ 27 cm + √ [ (1296 + 729) cm² ] ;
= π * (27 cm) * [ 27 cm + √ (2025 cm² ] ;
= π * (27 cm) * [ 27 cm + √ (2025 cm² ] ;
= π * (27 cm) * [ 27 cm + 45 cm ] ;
= π * (27 cm) * [ 27 cm + 45 cm ] ;
= π * (27 cm) * [ 72 cm ] ;
= π * (27 cm) * [ 72 cm ] ;
= (27 * 72) * π cm² ;
= (27 * 72) * π cm² ;
= " 1,944 π cm² " .
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Answer: [A]: " 1944 pi cm sq" .
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The exact surface area of the given "right cylinder" is: " 1,944 π cm² " .
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