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 to model the situation.
(b)How much should he take from each dimension?
Answers
Given:
Anshuman is preparing to make an ice sculpture.
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.
To find:
(a)Write a polynomial equation to model the situation.
(b)How much should he take from each dimension?
Solution:
From given, we have,
3 * 4 * 5 is the given dimension
Anshuman shaves off the same amount from the length width and height.
Let us say each side shaved = x ft
Length of the ice block remained = 5 - x ft
Width of the ice block remained = 3 - x ft
Height of the ice block remained = 4 - x ft
Volume of remained = ( 5 - x)(3 - x) (4 - x) cubic feet
= (5 - x) (12 - 7x + x²)
= ( 60 - 47x + 12x² - x³)
60 - 47x + 12x² - x³ = 24
x³ - 12x² + 47x = 36
x³ - 12x² + 47x - 36 = 0
x = 1 is the required value
(3 - 1) * (4 - 1) * (5 - 1) = 2 * 3 * 4 is the new dimension
The volume of block = 2 * 3 * 4 = 24
(a) x³ - 12x² + 47x - 36 = 0 is a polynomial equation to model the situation.
(b) 1 ft he should take from each dimension to reduce the volume of the ice block to 24 cubic feet.
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
Learn more:
write a cubic polynomial whose zeroes are add up to 12 and are in ...
https://brainly.in/question/18998065
. If the zeroes of the cubic polynomial f(x) = kx3 – 8x2 + 5 are alpha ...
https://brainly.in/question/10004198
https://brainly.in/question/12060218
