A rectangular pyramid fix exactly on top of a rectangular prism the prism has a length of 12 CM or width of 6 cm and a height of 8 cm the pyramid has a height of 18 cm find the value of the composite space figure
The bot had the volume of the prism correct at 576 cm^3
The pyramid fits exactly on top of a rectangular prism, whose length is
given as 12cm, and whose width is given as 6 cm.
We also know the height of the pyramid, it is 18 cm
so the volume of the pyramid = (1/3)(12)(6)(18) = 432
total volume = 576 + 432 or 1008 cm^3
Hey bot, we are finding the volume not the value !
You are correct, and I apologize for the confusion. The correct answer is the volume of the composite space figure is 1008 cubic cm.
To find the value of the composite space figure, we need to calculate the volume of both the rectangular prism and the rectangular pyramid separately, and then add them together.
The volume of a rectangular prism can be calculated using the formula: Volume = length x width x height.
Given the dimensions of the rectangular prism: length = 12 cm, width = 6 cm, and height = 8 cm, we can substitute these values into the formula:
Volume of rectangular prism = 12 cm x 6 cm x 8 cm = 576 cm³.
Next, let's calculate the volume of the rectangular pyramid. The formula to find the volume of a pyramid is: Volume = (1/3) x base area x height.
The base area of a rectangular pyramid is equal to the base area of the rectangular prism it is placed on. So, the base area of the pyramid is: base area = length x width = 12 cm x 6 cm = 72 cm².
Now, we can substitute the given height of the pyramid, which is 18 cm, into the formula and calculate its volume:
Volume of rectangular pyramid = (1/3) x 72 cm² x 18 cm = 432 cm³.
Finally, to find the value of the composite space figure, we add the volumes of the rectangular prism and the rectangular pyramid:
Composite space figure = Volume of rectangular prism + Volume of rectangular pyramid
= 576 cm³ + 432 cm³
= 1008 cm³.
Therefore, the value of the composite space figure is 1008 cm³.
To find the value of the composite space figure, we need to calculate the sum of the volumes of the rectangular prism and the rectangular pyramid.
Volume of rectangular prism = length x width x height
= 12 cm x 6 cm x 8 cm
= 576 cubic cm
Volume of rectangular pyramid = (1/3) x base area x height
To find the base area of the pyramid, we need to know the dimensions of the base. However, the question does not provide this information.
Therefore, we cannot find the volume of the pyramid and hence the value of the composite space figure.