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Vesnalui [34]
3 years ago
5

Circumference, radius, slant height, lateral area, and surface area are measurements of a cone. Given two of the measurements, f

ind the other three to the nearest tenth. r = 3 ft, S.A. = 50 ft.^2 Also: C = 44 in, L.A. = 176 in.^2
Mathematics
1 answer:
USPshnik [31]3 years ago
4 0

Answer:

  1. LA = 21.7 ft²; C = 18.8 ft; h = 2.3 ft
  2. h = 8 in; r = 7 in; SA = 330.1 in²

Step-by-step explanation:

Applicable relations are ...

  C = 2πr . . . . . . . r = radius, C = circumference

  LA = 1/2·Ch . . . . h = slant height, LA = lateral area

  SA = πr² +LA . . . SA = total surface area

__

1. Given r and SA, we can find the other measures as ...

  LA = SA -πr² = 50 ft² -π(3 ft)² ≈ 21.7 ft²

  C = 2πr = 2π(3 ft) ≈ 18.8 ft

  h = 2·LA/C ≈ 2·21.7 ft²/(18.8 ft) ≈ 2.3 ft

(Please note that for calculations using intermediate results, we used the full-precision values of those results, not the rounded ones. Rounding is always the last operation. Please note, too, that we have used a value for π sufficient to ensure accuracy in all the digits shown here.)

__

2. Given C and LA, we can find the other measures as ...

  h = 2·LA/C = 2(176 in²)/(44 in) = 8 in

  r = C/(2π) = (44 in)/(2π) ≈ 7.0 in

  SA = LA +πr² = LA +rC/2 ≈ 176 in² +(7.0 in)(44 in)/2 ≈ 330.1 in²

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Represent the length of one side of the base be s and the height by h.  Then the volume of the box is V = s^2*h; this is to be maximized.

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