A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length of 18cm, a width of 6cm, and a height of 9cm. The pyramid has a height of 15 cm. Find the volume of the composite figure.
504 cm^3
1,512 cm^3
1,620 cm^3
2,592 cm^3
First, we need to find the base area of the pyramid. Since it is a rectangle, we can use the formula for the area of a rectangle: base x height. The base of the pyramid is the same as the base of the prism, which is 18cm x 6cm = 108cm^2.
To find the volume of the pyramid, we use the formula: 1/3 x base area x height. Substituting in the values we know, we get:
1/3 x 108cm^2 x 15cm = 540cm^3
Next, we can find the volume of the prism using the formula: length x width x height.
18cm x 6cm x 9cm = 972cm^3
To find the total volume of the composite figure, we add the volume of the pyramid to the volume of the prism:
540cm^3 + 972cm^3 = 1,512cm^3
Therefore, the answer is 1,512 cm^3.