Question

A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y = ax? about the y-axis. If the dish is to have a 10-ft diameter and a maximum depth of 3 ft, find the value of a and the surface area S of the dish. (Round the surface area to two decimal places.) S-

Answer 1

Q. A group of engineers building a parabolic satellite dish whose Shape will be formed by rotating the curve y = ax? about the y-axis. If the dish is to 10-ft diameter and a maximum depth of 3 ft, find the value of a and the surface Arca s of the dish have a solution is Radius of a Satellite dish 10 2. 5 ft Given pasabolic equation Y = ax? رن. when x=57t then y=3 tt 3= a (5) aa 3 25 Answer put the value of in cqri y= 3 x² 2s taking both side differentiation dy 25 6 dx We can use for rotation about the y-axis Safanud Where ds - to + Cez y dx YOS S 11+/dy dx X=0

5 S =25 30 1+ 36 (² 3600 da 625 Lot 36x² 625 dt = 0+ 72 x dx 625 Xdx 625 dt 73 When then t=1 Y = 5 then tu + - 1 + 36 x 35 625 36 25 to 61 25 25 fs 20 X 625 at 72 625 625 T 36 ✓t dt 3/ 372 3/2 SE 625 ñ 36 625x20 368 3 61 ২S *-09 312 3.8114 = 102. 22 ft n 625 A 54 -] S 101.22. ft? Answer

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