Answer: the height of the prism is 14 cm.
Step-by-step explanation:
The formula for determining the volume of a rectangular prism is expressed as
Volume = length × height × width
Volume = LWH
The length of the prism is 3 times the width. It means that
L = 3W
The height is twice the width. This means that
H = 2W
Therefore,
Volume = 3W × × W × 2W = 6W³
The volume of a rectangular prism is 2,058 cubic cm. This means that
2058 = 6W³
Dividing through by 6, it becomes
343 = W³
W = 7
Therefore, the height of the prism would be
H = 2W = 2 × 7
H = 14 cm
