A rectangular pyramid fits exactly on top of a rectangular prism. Find the volume of the composite space figure if the prism has length 19 cm, width 2 cm, height 11 cm, and the pyramid has height 7 cm.
To find the volume of the composite space figure, we need to find the volumes of the rectangular prism and the rectangular pyramid separately, and then add them together.
First, let's find the volume of the rectangular prism. The formula for the volume of a rectangular prism is:
Volume = Length x Width x Height
Substituting the given values, we have:
Volume of the rectangular prism = 19 cm x 2 cm x 11 cm
Next, let's find the volume of the rectangular pyramid. The formula for the volume of a pyramid is:
Volume = 1/3 x Base Area x Height
Since the base of the pyramid is a rectangle, the base area is given by:
Base Area = Length x Width
Substituting the given values, we have:
Base Area = 19 cm x 2 cm
Now, let's calculate the volume of the rectangular pyramid:
Volume of the rectangular pyramid = 1/3 x (19 cm x 2 cm) x 7 cm
Finally, we can find the volume of the composite space figure by adding the volume of the rectangular prism and the volume of the rectangular pyramid:
Volume of the composite space figure = Volume of the rectangular prism + Volume of the rectangular pyramid
You can use a calculator to perform the calculations and find the final volume.