Answer:
Side length of the box: 6 cm
Volume of the box/cube: 216 cm³
Volume of the box without cone: 190.88 cm³
Explanation:
The sides of a cube are all equal, so in this case, the side length of the box is 6 cm.
Then, the volume can be calculated as
Volume = side x side x side
Volume = 6 cm x 6 cm x 6 cm
Volume = 216 cm³
To know the volume of the box with the cone shape cut of it, we need to calculate the volume of the cone with the following equation
[tex]Volume=\frac{1}{3}\pi r^2h[/tex]Where π = 3.14, r is the radius and h is the height. The diameter of the cone is 4 cm, so the radius is
r = 4 cm/2 = 2 cm
Then, replacing r = 2 cm and h = 6 cm, we get
[tex]\begin{gathered} Volume=\frac{1}{3}(3.14)(2\text{ cm\rparen}^2(6\text{ cm\rparen} \\ Volume=\frac{1}{3}(3.14)(4\text{ cm}^2)(6\text{ cm\rparen} \\ Volume=25.12\text{ cm}^3 \end{gathered}[/tex]Now, the volume of the box without the cone shape is
V = 216 cm³ - 25.12 cm³
V = 190.88 cm³
So, the answers are
Side length of the box: 6 cm
Volume of the box/cube: 216 cm³
Volume of the box without cone: 190.88 cm³