a jewlery box in the shape of a rectangle prism has a volume of 90in.3 and a height of 2 1/2 in, What are possible demensions for the length and width of base
Roy made a jewelry box in the shape of a rectangular prism with the dimensions shown.
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Find the volume of the jewelry box.
To determine the possible dimensions for the length and width of the base of the jewelry box, we need to use the formula for the volume of a rectangular prism: volume = length x width x height.
Given that the volume is 90 in³ and the height is 2 1/2 in, we can substitute the known values into the formula:
90 in³ = length x width x (2 1/2) in
Since 2 1/2 can also be written as 5/2, we have:
90 in³ = length x width x (5/2) in
To find the possible dimensions for the length and width, let's assume one of them and solve for the other. We'll start by assuming a length value and solve for the corresponding width.
Case 1: Assume the length is 9 in.
Substituting the assumed length into the equation:
90 in³ = 9 in x width x (5/2) in
Simplifying:
90 in³ = (45/2) in² x width
Dividing both sides by (45/2) in²:
90 in³ ÷ (45/2) in² = width
Simplifying:
90 in³ x (2/45 in²) = width
4/1 in² = width
Therefore, when the length is 9 in, the width is 4 in.
Case 2: Assume the length is 6 in.
Substituting the assumed length into the equation:
90 in³ = 6 in x width x (5/2) in
Simplifying:
90 in³ = (30/2) in² x width
Dividing both sides by (30/2) in²:
90 in³ ÷ (30/2) in² = width
Simplifying:
90 in³ x (2/30 in²) = width
6/1 in² = width
Therefore, when the length is 6 in, the width is 6 in.
The possible dimensions for the length and width of the base of the jewelry box are: 9 in x 4 in and 6 in x 6 in.