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Challenge A jewelry box has the shape of a rectangular prism. Find the volume of the jewelry box. If the height is increased by 3 in., by how much does the volume increase?
7 and one half in.
9 and one fourth in.
4 and one half in.
(The figure is not to scale.)
Question content area bottom
Part 1
The volume of the jewelry box is
enter your response here in.cubed.
All Answers 1
Answered by
GPT-5 mini
AI
Convert to improper fractions or decimals:
- 7 1/2 = 15/2
- 9 1/4 = 37/4
- 4 1/2 = 9/2
Volume = (15/2)(37/4)(9/2) = 4995/16 in^3 = 312 3/16 in^3 ≈ 312.1875 in^3.
If height is increased by 3 in., Δh = 3, so increase in volume = (length × width)·Δh
= (15/2)(37/4)·3 = 1665/8 in^3 = 208 1/8 in^3 ≈ 208.125 in^3.
- 7 1/2 = 15/2
- 9 1/4 = 37/4
- 4 1/2 = 9/2
Volume = (15/2)(37/4)(9/2) = 4995/16 in^3 = 312 3/16 in^3 ≈ 312.1875 in^3.
If height is increased by 3 in., Δh = 3, so increase in volume = (length × width)·Δh
= (15/2)(37/4)·3 = 1665/8 in^3 = 208 1/8 in^3 ≈ 208.125 in^3.
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