The answer is: "527.52 [square yards]"
.
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Explanation:
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Surface Area (S.A. of a cone) = π *r * (r + √(h² + r²) ;
in which: π = 3.14 (as instructed in the given problem;
r = radius = diameter / 2 = 14 yd / 2 = 7 yd.
(Note: diameter = 14 yd ; given in the figure shown) ; h = perpendicular height = ??
Let us use the Pythagorean theorem to determine "h" (the perpendicular
height);
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a² + b² = c² ; in which "c" in the hypotenuse;
c = 17 yd. (the "slant length" of the cone; given in the figure);
Let: "b" = the radius, "r" = 7 yd;
Solve for "a"; which is the "perpendicular height" ; or "h" ;
→ a² + b² = c² ;
→ a² = c² − b² ;
→ Plug in our known values for "c" and "b" ; to solve for "a" ;
→ a² = 17² − 7² = 289 − 49 = 240 ;
→ a² = 240 ;
Take the positive "square root" of each side of equation; to isolate "a" on one side of the equation" and to solve for "a" ;
→√(a²) = √240 ;
→ a = 15.4919333848296675 ; = "h" ; perpendicular height;
For now, we can simply refer to: "h" as equal to: "(√240)" ;
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Now, given the formula for the surface area of a cone:
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→ " Surface Area (S.A. of a cone) = π *r * (r + √(h² + r²) " ;
Plug in our known values; and solve:
→Surface Area (S.A. of a cone) =
3.14 * (7 yd) * { 7 yd + √[(√240)² + (7 yd)²] } ;
= 3.14 * (7 yd) * { 7 yd + √[(240 + (49 yd²] } ;
= 3.14 * (7 yd) * { 7 yd + √289 yd²} ;
= 3.14 * (7 yd) * ( 7 yd + 17 yd) ;
= 3.14 * (7 yd) * (24 yd)
= 527.52 yd² ; or write as: "527.52 square yards".
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