Question

Circumference, radius, slant height, lateral area, and surface area are measurements of a cone. Given two of the measurements, find the other three to the nearest tenth. r = 3 ft, S.A. = 50 ft.^2 Also: C = 44 in, L.A. = 176 in.^2

Answer 1

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

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

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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.)

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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