rachel has a box in the shape of a rectangular prism the length of the box is 3 feet the width is 1.5 feet, and the height is 1 foot. what is the volume of the box measured in cubic inches ?
Answers
Answered by
0
volume of square based prism = a²h
therefore
150 in³ = x²y
y = 1.5x
150 = 1.5x³
100 = x³
x = ³√100 ≈ 4.64 in
y = 1.5x ≈ 6.96 in
Answered by
1
Answer:
Step-by-step explanation:
Box = Prism Shape = square base (Given)
Volume = 150 in³ (Given)
Equation of volume = V = s²h
= 150 = s²h
Height of the box = 3/2 times the base length, thus -
= h = (3/2)s
Substituting the value into the volume equation, and solving for s -
= 150 = s²h
= 150 = s²(3/2)s
= (2/3)150 = s³
= 100 = s³
s = ∛100 (approx 4.642 in)
Now since we the value for s, we can solve for h -
h = (3/2)∛100 (approx 6.962 in)
Therefore, the approximate height and the length of the box is x = 4.6 and y = 6.9.
Similar questions