1. Algebra 1 Item No. 48
A square cardboard (see diagram) is designed to
form a container. A 2 inch square is cut off on
each corner. The container can hold 288 cubic
inches. Find the perimeter of the square.
A.8 in C. 32 in
B. 16 in D. 64 in
www.upcatreview.com
2 in.
2 in.
2 in.
2. 2 in.
2 in.
2 in.
Volume of container = 288 cm3
To solve the problem, we must first visualize
the given situation:
www.upcatreview.com
3. We then make a representation of the
unknown: Let x be the length of the side
of the cardboard.
2 in.
2 in.
2 in.
x x โ 4
By subtracting 2 inches from
both ends of the side, we get
the representation for the boxโs
length and width, x โ 4
www.upcatreview.com
4. The cardboard will be folded and will then
be made into a box like so:
2 in.
Volume of container = 288 cm3
This will be the
height of the
container.
This will be the length (and
also the width) of the
container.
www.upcatreview.com
x โ 4
5. We will use the formula in finding the
volume:
V = LWH
www.upcatreview.com
6. We will use the formula in finding the
volume:
V = LWH
The length L can be expressed in terms of x:
L = x โ 2 โ 2 or L = x โ 4
www.upcatreview.com
7. We will use the formula in finding the
volume:
V = LWH
The length L can be expressed in terms of x:
L = x โ 2 โ 2 or L = x โ 4
Same is true for the width W:
W = x โ 2 โ 2 or W = x โ 4
www.upcatreview.com
8. We will use the formula in finding the
volume:
V = LWH
The length L can be expressed in terms of x:
L = x โ 2 โ 2 or L = x โ 4
Same is true for the width W:
W = x โ 2 โ 2 or W = x โ 4
The height H of the container would be 2 inches.
www.upcatreview.com
9. Putting everything in its proper place in the
equation, we have:
2
)4(144
2)4)(4(288
โ=
โโ=
=
x
xx
LWHV
www.upcatreview.com
10. Putting everything in its proper place in the
equation, we have:
Solving the quadratic equation by getting the
square root of both sides, we get:
2
)4(144
2)4)(4(288
โ=
โโ=
=
x
xx
LWHV
8or16
124
4144
โ==
=ยฑ
โ=ยฑ
xx
x
x
We reject the
negative solution.
www.upcatreview.com
11. Note that x = 16 is NOT yet the final answer.
We should always remember that we
have to check whether we have answered
the real question in the item.
www.upcatreview.com
12. Note that x = 16 is NOT yet the final answer.
We should always remember that we
have to check whether we have answered
the real question in the item.
We are asked for the perimeter. To obtain it:
in64
)16(4
4
=
=
= sPerimeter
www.upcatreview.com
14. Algebra 1 Item No. 48
A square cardboard (see diagram) is designed to
form a container. A 2 inch square is cut off on
each corner. The container can hold 288 cubic
inches. Find the perimeter of the square.
A.8 in C. 32 in
B. 16 in D. 64 in
2 in.
2 in.
2 in.
www.upcatreview.com
