Consider how you could alter each dimension to double the volume.
D
d
Calculate the volume of Model C. Divide the volume of Model A by the result.
A
a
500 ft^2
B
b
25 ft * 20 ft * 3.5 ft
C
c
See solution.
D
d
1 : 4
Practice makes perfect
a
To begin we need to convert the depth, or height, into feet so that all measurements use the same units.
42÷12= 3.5Next, we can substitute the given values for depth and volume into the volume of a prism.
Depth=& 3.5
Volume=& 1750
V=& B h
⇕&
1750=&B ( 3.5)
Finally, we divide the equation by the depth. The result will be the surface area.
Finally, we set each factor equal to 0 and solve for w.
rcl
(w+25)=0 &⇒ & w=-25
(w-20)=0 &⇒ & w=20
The width cannot be negative so we can disregard -25. Therefore, the width is 20ft. The length is 5ft greater than the width, or 25ft. We were given the depth, which is 3.5ft
c
Since the volume is doubled, we can double any single dimension.
50 * 20 * 3.5 = 3500
25 * 40 * 3.5 = 3500
25 * 20 * 7 = 3500
There are other possible dimensions as well these are just some examples.
d
We need to start by calculating the volume of Model C. We will multiply the length and width both by 2.
25(2) * 20(2) * 3.5
⇕
50 * 40 * 3.5 = 7000
Now, we can create a ratio using the volume of Model A and Model C.
1750/7000 ⇒ 1 : 4
