A propane storage tank for a home is shaped like a cylinder with hemispherical ends, and a cylindrical portion length that is 4 times the radius.
The formula S=12pi(3V/16pi)^(2/3) expresses the surface area of a tank with this shape in terms of its volume.
A. Use the properties of rational exponents to rewrite the expression for the surface area so that the variable V is isolated. Then write the approximate model with the coefficient rounded to the nearest hundredth.
B. What is the surface area in square feet for a tank with a volume of 150 ft^2?
+130514 I'm assuming this is supposed to be :
S=12pi(3V/[16pi])^(2/3)
(A) exponentiate both sides to the 3/2 power
S^(3/2) = 12pi ( 3V/[ 16 pi])
S^(3/2) = (36/16) V
S^(3/2) = ( 9/4)V
S^(3/2) = 2.25V
[ S^(3/2)] / 2.25 = V
(1 / 2.25)S^(3/2) = V
[0.44]S^(3/2) = V [the 0.44 is the "rounded" coefficient]
(B) 12pi(3[150]/[16pi])^(2/3) = about 162.54 sq ft
BTW - this is correct based on my interpretation of the formula......if the "pi" in the parentheses in the formula was not supposed to be in the denominator, a clearer form would have been :
S = S=12pi[ (3/16)Vpi ] ^(2/3).........I did not interpret it in that way.......I interpreted "16 pi" as the whole denominator
