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?
6 1/2in 9 1/4in 5 1/2in
To find the volume of the jewelry box, we will multiply the length, width, and height of the box together.
Given:
Length = 6 1/2 inches
Width = 9 1/4 inches
Height = 5 1/2 inches.
To convert the mixed numbers into improper fractions:
Length = 6 1/2 = (2*6 + 1)/2 = 13/2
Width = 9 1/4 = (4*9 + 1)/4 = 37/4
Height = 5 1/2 = (2*5 + 1)/2 = 11/2
So, Volume = (length)(width)(height) = (13/2)(37/4)(11/2)
To multiply the fractions, we will multiply the numerators together and the denominators together:
Volume = (13*37*11) / (2*4*2)
= 5797 / 16
= 361.06 cubic inches (rounded to two decimal places).
Now, the height is increased by 3 inches, which means the new height is 5 1/2 + 3 = 8 1/2 inches.
To find the increase in volume, we need to find the difference between the new volume and the original volume.
New Volume = (length)(width)(new height)
= (13/2)(37/4)(17/2)
Volume Increase = New Volume - Original Volume
= (13/2)(37/4)(17/2) - (13/2)(37/4)(11/2)
To simplify these expressions, we can cancel out common factors:
Volume Increase = [(13*37*17) / (2*4*2)] - [(13*37*11) / (2*4*2)]
Now, calculate the volume increase to find the final answer.