Rekha wants to make a pencil box using a cardboard. When searching she got a cardboard with sides 12inch by 12 inch. She cuts out four squares of equal size at corners and folding up the sides. She paints it beautifully and puts all her pencils in that. Suppose the side of the square cutout in x inch. Give the polynomial to find the volume of the cuboid formed. And identify the degree of the polynomial.
Answers
Solution :-
From image we can see that , we have given :-
- A cardboard in the shape of Square of side = 12 inch .
- four squares of equal size at corners are cut with side as = x inch .
As we can see that, when 2 Square with side x inch are cut from one side of cardboard , than , Length of Cardboard Left is :- (12 - 2x) inch .
Similarly,
→ Breadth of cardboard Left = (12 - 2x) inch .
Now, when this shape is fold up the sides , it formed a cuboid with :-
→ Length of cuboid = Length of Cardboard Left = (12 - 2x) inch .
→ Breadth of cuboid = Breadth of Cardboard Left = (12 - 2x) inch .
→ Height of cuboid = Side of Square cut along the corners = x inch .
Therefore,
→ Volume of cuboid = Length * Breadth * Height
→ Volume = (12 - 2x) * (12 - 2x) * x
→ volume = (12 - 2x)² * x
using (a - b)² = (a² + b² - 2ab)
→ volume = (144 + 4x² - 48x) * x
→ volume = (4x³ - 48x² + 144x) .
Hence, the polynomial to find the volume of the cuboid formed is (4x³ - 48x² + 144x) .
And,
→ Degree of This Polynomial = The highest degree of the variable in a polynomial expression = 3. (cubic Polynomial.)
AnswEr:-
When 2 Square with side x inch are cut from one side of cardboard , than , Length of Cardboard Left is :- (12 - 2x) inch .
Similarly,
→ Breadth of cardboard Left = (12 - 2x) inch .
Now, when this shape is fold up the sides , it formed a cuboid with :-
→ Length of cuboid = Length of Cardboard Left = (12 - 2x) inch .
→ Breadth of cuboid = Breadth of Cardboard Left = (12 - 2x) inch .
→ Height of cuboid = Side of Square cut along the corners = x inch .
Therefore,
→ Volume of cuboid = Length * Breadth * Height
→ Volume = (12 - 2x) * (12 - 2x) * x
→ volume = (12 - 2x)² * x
using (a - b)² = (a² + b² - 2ab)
→ volume = (144 + 4x² - 48x) * x
→ volume = (4x³ - 48x² + 144x) .
Hence, the polynomial to find the volume of the cuboid formed is (4x³ - 48x² + 144x) .
And,
→ Degree of This Polynomial = The highest degree of the variable in a polynomial expression = 3. (cubic Polynomial.)
-______________________________________________________