A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length of 16 cm, a width of 6 cm, and a height of 8 cm. The pyramid has a height of 14 cm. Find the volume of the composite space figure.
Why did the rectangular pyramid go on a date with the rectangular prism? Because they wanted to pyramid scheme their love! Now let's calculate the volume of their composite space figure.
The volume of the prism can be found by multiplying its length, width, and height: V_prism = 16 cm * 6 cm * 8 cm = 768 cm³.
Since the rectangular pyramid fits exactly on top of the prism, its base dimensions will be the same as the top face of the prism, which is 16 cm by 6 cm. The volume of the pyramid can be found by multiplying the base area by the height and dividing by 3: V_pyramid = (16 cm * 6 cm * 14 cm) / 3 = 1792 cm³.
To find the volume of the composite space figure, we add the volumes of the prism and the pyramid: V_composite = V_prism + V_pyramid = 768 cm³ + 1792 cm³ = 2560 cm³.
So, the volume of the composite space figure is 2560 cm³. That's pyramid-tastic!
To find the volume of the composite space figure, we first need to find the volume of the rectangular prism and the volume of the rectangular pyramid separately, and then add them together.
Volume of the rectangular prism = length * width * height
= 16 cm * 6 cm * 8 cm
= 768 cm^3
Volume of the rectangular pyramid = (1/3) * base area * height
= (1/3) * (length * width) * height
= (1/3) * (16 cm * 6 cm) * 14 cm
= (1/3) * 96 cm^2 * 14 cm
= 448 cm^3
Now, to find the volume of the composite space figure, we add the volumes of the rectangular prism and the rectangular pyramid together.
Volume of the composite space figure = Volume of the rectangular prism + Volume of the rectangular pyramid
= 768 cm^3 + 448 cm^3
= 1216 cm^3
Therefore, the volume of the composite space figure is 1216 cm^3.
To find the volume of the composite space figure, we need to first find the individual volumes of the rectangular prism and the rectangular pyramid, and then add them together.
The volume of a rectangular prism is given by the formula:
Volume = Length * Width * Height
In this case, the length of the prism is 16 cm, the width is 6 cm, and the height is 8 cm. So, the volume of the prism is:
Volume of prism = 16 cm * 6 cm * 8 cm = 768 cm³
Next, let's find the volume of the rectangular pyramid. The volume of a pyramid is given by the formula:
Volume = (1/3) * Base Area * Height
In this case, since the base of the pyramid is a rectangle, the base area is equal to the length multiplied by the width. So, the base area of the pyramid is:
Base Area = Length * Width = 16 cm * 6 cm = 96 cm²
The height of the pyramid is given as 14 cm. So, the volume of the pyramid is:
Volume of pyramid = (1/3) * 96 cm² * 14 cm = 448 cm³
Finally, to find the volume of the composite space figure, we add the volume of the prism and the volume of the pyramid:
Volume of composite space figure = Volume of prism + volume of pyramid = 768 cm³ + 448 cm³ = 1216 cm³
Therefore, the volume of the composite space figure is 1216 cm³.
The base B = 16*6
prism: v = B*8
pyramid: v = 1/3 * B * 14