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 1/2in tall 9 1/4 long 5 1/2 depth
To find the volume of the jewelry box, we multiply the length, width, and height together.
Volume = length * width * height
Given the dimensions:
Length = 9 1/4 inches
Width = 5 1/2 inches
Height = 7 1/2 inches
Converting the mixed numbers to improper fractions:
Length = 37/4 inches
Width = 11/2 inches
Height = 15/2 inches
Calculating the volume:
Volume = (37/4) * (11/2) * (15/2)
Volume = (37 * 11 * 15) / (4 * 2 * 2)
Volume = 11235 / 16
Volume ≈ 702.19 cubic inches
If the height is increased by 3 inches, the new height will be:
New Height = 7 1/2 + 3 = 15/2 + 6/2 = 21/2 inches
Calculating the new volume with the increased height:
New Volume = (37/4) * (11/2) * (21/2)
New Volume = (37 * 11 * 21) / (4 * 2 * 2)
New Volume = 86253 / 16
New Volume ≈ 5390.81 cubic inches
The volume increases by:
Increase = New Volume - Volume
Increase = 5390.81 - 702.19
Increase ≈ 4688.62 cubic inches
Therefore, the volume of the jewelry box increases by approximately 4688.62 cubic inches.