A closed box in the shape of a cuboid has dimensions x cm, y cm and 5 cm.
The volume of the box is 40 cm^3 and the external surface area is 76 cm^2.
A) use the information about the volume to find and equation connecting x and y
B) use the information about the external surface area to find another equation connecting x and y.
C) solve the equations simultaneously.
I just need help with part A and B.
Thank you.
:)
A) since V = lwh
5xy = 40
xy = 8 or y = 8/x
B)
surface area = 2xy + 2(5x) + 2(5y) = 76
xy + 5x + 5y = 38
x(8/x) + 5x + 5(8/x) = 38
8 + 5x + 40/x = 38
5x + 40/x = 30
C)
times x
5x^2 - 30x + 40 = 0
x^2 - 6x + 8 = 0
(x-4)(x-2) = 0
x = 4 or x= 2
if x=4, y=2
if x=2, y=4
or we can just say the base is 4 by 2
A) To find an equation connecting x and y using the information about the volume, we need to use the formula for the volume of a cuboid, which is given by:
Volume = length * width * height
Given that the volume is 40 cm^3 and the dimensions of the box are x cm, y cm, and 5 cm, we can set up the equation:
40 = x * y * 5
Simplifying the equation, we get:
200 = 5xy
So, the equation connecting x and y based on the volume information is:
5xy = 200
B) To find another equation connecting x and y using the information about the external surface area, we need to find the formula for the surface area of a cuboid. The surface area of a rectangular prism is given by:
Surface Area = 2lw + 2lh + 2wh
Given that the external surface area is 76 cm^2 and the dimensions of the box are x cm, y cm, and 5 cm, we can set up the equation:
76 = 2xy + 2x(5) + 2y(5)
Simplifying the equation, we get:
76 = 2xy + 10x + 10y
Rearranging the equation, we get:
10x + 2xy + 10y = 76
So, the equation connecting x and y based on the external surface area information is:
10x + 2xy + 10y = 76
Now you have two equations, one based on volume (5xy = 200) and another based on external surface area (10x + 2xy + 10y = 76), which you can solve simultaneously in part C.