A coconut is a fruit that is made up of a hard outer shell that is spherical. Inside, there is a thick layer of coconut meat that forms another spherical shell around the coconut milk. If the diameter of an entire coconut is 5 inches, and the coconut meat is 1 inch thick, then there is room for approximately _[blank]_ in3 of coconut milk. What number correctly fills in the blank in the previous sentence? Hint: Find the radius of the inside sphere and use that to calculate the volume. Use 3.14 for π and round your answer to the nearest hundredth, if necessary, like this: 42.53 PLEASE HELP!!!

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)

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