Answer:
(a) 1870 cubes; (b) 233¾ in³
Step-by-step explanation:
Data:
l = 11 in
w = 8½ in
h = 2½ in
(a) Volume of box in cubes
Convert each dimension of the box to cubes
l = 11 ÷ ½ = 11 × 2 = 22 cubes
w = 8½ ÷ ½ = 8½ × 2 = 16 + 1 = 17 cubes
h = 2½ ÷ ½ = 2½ × 2 = 4 + 1 = 5 cubes
Calculate the volume of the box
V = lwh = 22 × 17 × 5 = 1870 cubes
The box can contain 1870 cubes.
(b) Volume of box in cubic inches
Calculations:
V = 11 × 8½ × 2½
Convert each number to an improper fraction:
[tex]\frac{11 }{1 }\times \frac{17 }{2 } \times \frac{5 }{2 }[/tex]
Multiply the numerators and multiply the denominators
[tex]\frac{11 \times 17 \times 5 }{4 } = \frac{935 }{4 }[/tex]
Convert the answer back to a mixed number
[tex]\frac{935 }{ 4} =\text{233r3}[/tex] (233 with a remainder of 3)
The volume of the box is 233¾ in³.
