A square piece of cardboard is y = 15 inches long on each side. From each corner a square piece x inches on a side is cut out as shown. The flaps are then turned up to form an open box. Find a polynomial that represents the volume of the box.
A) $225 x - 60 x ^ { 2 } + x ^ { 3 }$
B) $225 - 60 x + 4 x ^ { 2 }$
C) $225 x - 60 x ^ { 2 } + 4 x ^ { 3 }$
D) $225 x - 15 x ^ { 2 } + 4 x ^ { 3 }$
E) none of these

Question

A square piece of cardboard is y = 15 inches long on each side. From each corner a square piece x inches on a side is cut out as shown. The flaps are then turned up to form an open box. Find a polynomial that represents the volume of the box. 
A) $225 x - 60 x ^ { 2 } + x ^ { 3 }$ 
B) $225 - 60 x + 4 x ^ { 2 }$ 
C) $225 x - 60 x ^ { 2 } + 4 x ^ { 3 }$ 
D) $225 x - 15 x ^ { 2 } + 4 x ^ { 3 }$ 
E) none of these

Quizplus · Accepted Answer

To find the volume of the box, we need to find the area of the base and multiply it by the height of the box. The base of the box is a square with side length (15 - 2x) inches, since x inches are cut out from each corner. The height of the box is simply x inches. Therefore, the volume of the box is:
V = (15 - 2x)^2 * x
Expanding and simplifying, we get:
V = 225x - 60x^2 + 4x^3
Which matches choice C.

A Square Piece of Cardboard Is Y = 15 Inches 225x−60x2+x3225 x - 60 x ^ { 2 } + x ^ { 3 }225x−60x2+x3

A Square Piece of Cardboard Is Y = 15 Inches $225 x - 60 x ^ { 2 } + x ^ { 3 }$