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The canvas wind shelter is to be constructed for use on Padre Island beaches. It is to have a back, two square sides, and a top. If 216 square feet of canvas are available, find the length of the shelter for which the volume inside is maximized assuming all the canvas is used.

Respuesta :

Answer:

6 ft, 6 ft, 12 ft

Step-by-step explanation:

Area = 216 sq feet

let the sides are y, y and z.

Area, A = 2y² + 2yz

216 = 2y² + 2yz

108 = y² + yz

z = (108 - y²) / y     .... (1)

Volume, V = y²z  

Substitute the values of z from equation (1)

V = 108 y - y³

Differentiate with respect to y

dV/dy = 108 - 3y²

Put it equal to zero for maxima and minima

3y² = 108

y = 6 ft

So, z = (108 - 36) / 6 = 12 ft

Thus, the sides are 6 ft, 6 ft, 12 ft.

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