Solve.
1. Five metal cubes with sides of 5 cm were melted and casted into a bigger cube. Find the volume of the new cube.
Solution:
Formula: V = x³
V = 5³
V = (5) (5) (5)
V = (25) (5)
V = 125 cm³
2. How much salt is needed to fill a pit that is 10 m deep, 8 m wide, and 12 m long?
Solution:
Formula: V = L * w * h
V = 12 * 8 * 10
V = 96 * 10
V = 960 cm³
3. A cubical box with dimensions 8 cm by 6 cm by 12 cm is melted into another cube whose width is 16 cm. Find the length and height of the new cube formed if l = h.
Answer: 6
Solution:
The volume of the rectangular cuboid:
V₁ = 8 * 6 * 12
V₁ = 48 * 12
V₁ = 576 cm³
After the cuboid is melted, whose width is 16 cm, the volume will be:
V₂ = 16 * l * h
Since l = h, V₂ = 16 * l * l or V₂ = 16l² will do.
V₁ = V₂
576 = 16l²
[tex]\frac{576}{16}=\frac{16\:l^{2}}{16}[/tex]
36 = l²
6 = l
Therefore, the length and height of the new cube formed is 6 cm.
4. Carlo found a big box filled with equal sizes of smaller sizes. If the big box measures 12 cm by 6 cm by 10 cm, how many smaller boxes have Carlo found if each of the smaller boxes measured 5 cm * 4 cm * 3 cm?
Answer: 12
Solution:
The volume of the 'big box':
V₁ = l * w * h
V₁ = 12 * 6 * 10
V₁ = 72 * 10
V₁ = 720 cm³
The volume of the 'smaller boxes':
V₂ = l * w * h
V₂ = 5 * 4 * 3
V₂ = 20 * 3
V₂ = 60 cm³
Now, to find how many smaller boxes Carlo found, we can divide the volume of the big box by the volume of the smaller box.
720 ÷ 60 = 12
Therefore, Carlo found 12 smaller boxes within the big box.
