Calculate the volume of the figure.
The figure is a box with measurements of base 3 cm...length 3 cm height 3 cm and then there is a pyramid on top of the box - perfect fit... but the height of the pyramid is 2 cm. is the volume 33 cm^3?
Thank you
To calculate the volume of the figure, we need to calculate the volume of the box and the volume of the pyramid separately and then add them together.
1. Calculate the volume of the box:
The volume of a box is calculated by multiplying the length, width, and height of the box. In this case, the base of the box has dimensions 3 cm x 3 cm, and the height of the box is 3 cm. So the volume of the box is:
Volume_box = base area x height = (3 cm x 3 cm) x 3 cm = 27 cm^3
2. Calculate the volume of the pyramid:
The volume of a pyramid is calculated by multiplying the base area of the pyramid by its height and then dividing by 3. In this case, the base of the pyramid is the same as the base of the box, with dimensions 3 cm x 3 cm, and the height of the pyramid is 2 cm. So the volume of the pyramid is:
Volume_pyramid = (base area x height) / 3 = ((3 cm x 3 cm) x 2 cm) / 3 = 18 cm^3
3. Add the volumes of the box and pyramid:
Volume_figure = Volume_box + Volume_pyramid = 27 cm^3 + 18 cm^3 = 45 cm^3
Therefore, the correct volume of the figure is 45 cm^3, not 33 cm^3.