Consider a rectangular box of volume 300 cubic centimters. Suppose that the base is a rectangle with sides x?

Question

Consider a rectangular box of volume 300 cubic centimeters. Suppose that the base is a rectangle with sides x centimeters and 3x centimeters. Let h(x) give the height of the box in centimeters and let A(x) be the total area of the six sides of the box.

The height of H(x)=__________cm

The surface area is A(x)=_______cubic cm

Answer 1

300 = x * 3x *h

h(x) = 300/ 3 x^2 = 100/x^2 cm

a(x) = 2(x* 3x) + 2(x*h) + 2(3x* h)

a(x) = 6x^2 + 800/x