Anshuman is preparing to make an ice sculpture. He has a block of ice as shown in figure that he wants to reduce in size by shaving off the same amount from the length width and height.He wants to reduce the volume of the ice block to 24 cubic feet.
(a)write a polynomial equation model this situation.
(b)How much should he take from each dimension?
Answers
Given : Anshuman is preparing to make an ice sculpture He wants to
reduce the volume of the ice block to 24 cubic feet.
To find : (a)write a polynomial equation to model this situation .
(b) how much should he take from each dimension
Solution:
Let say each side shaved = x ft
Length remained = 5 - x ft
Width remained = 3 - x ft
Height remained = 4 - x ft
Volume of remained = ( 5 - x)(3 - x) (4 - x) cubic feet
= (5 - x) (12 - 7x + x²)
= ( 60 - 47x + 12x² - x³) cubic feet
60 - 47x + 12x² - x³ = 24
=> x³ - 12x² + 47x = 36
=> x³ - 12x² + 47x - 36 = 0
x = 1 is the solution
He should take 1 ft from each side
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