6. 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.
10. What is the maximum volume of a square pyramid that can fit inside a cube with a side length of 14 cm?
pls help!! im behind and i don't understand
for each prism, volume = length*width*height
the height of the pyramid is equal to the side of the cube.
The base of the pyramid is the same as the base of the cube, so
v = 1/3 Bh = 1/3 * 14^3
how do i solve number 10?
I come here for answers and can't even find most of them wow
To find the volume of the composite space figure in question 6, we need to add the volumes of the rectangular prism and the rectangular pyramid.
Step 1: Calculate the volume of the rectangular prism.
The volume of a rectangular prism is given by the formula: volume = length × width × height.
In this case, the length is 16 cm, the width is 6 cm, and the height is 8 cm.
So, the volume of the rectangular prism is 16 cm × 6 cm × 8 cm = 768 cm³.
Step 2: Calculate the volume of the rectangular pyramid.
The volume of a rectangular pyramid is given by the formula: volume = (1/3) × base area × height.
In this case, the base of the rectangular pyramid is the same as the base of the rectangular prism, which is a rectangle with a length of 16 cm and a width of 6 cm. So, the base area is 16 cm × 6 cm = 96 cm².
The height of the pyramid is given as 14 cm.
Therefore, the volume of the rectangular pyramid is (1/3) × 96 cm² × 14 cm = 448 cm³.
Step 3: Add the volume of the rectangular prism and the rectangular pyramid.
768 cm³ + 448 cm³ = 1216 cm³.
Hence, the volume of the composite space figure is 1216 cm³.
Now let's move on to question 10.
To find the maximum volume of a square pyramid that can fit inside a cube, we need to consider the relationship between the side lengths of the pyramid and the cube.
Step 1: Understand the properties of a square pyramid and a cube.
A square pyramid is a pyramid with a square base, and a cube is a three-dimensional figure with six equal square faces. The base of the pyramid must fit exactly within the face of the cube.
Step 2: Determine the relationship between the side lengths of the square pyramid and the cube.
Since the base of the square pyramid must fit exactly within a face of the cube, the side length of the square pyramid must be equal to or smaller than the side length of the cube.
Step 3: Use the formula for the volume of a square pyramid.
The volume of a square pyramid is given by the formula: volume = (1/3) × base area × height.
In this case, the base is a square, so the base area is side length squared.
Step 4: Calculate the maximum volume of the square pyramid.
The side length of the cube is given as 14 cm. Therefore, the maximum side length of the square pyramid (and the base of the pyramid) is also 14 cm.
The height of the pyramid can be any value less than or equal to 14 cm.
Thus, the maximum volume of the square pyramid is (1/3) × (14 cm)² × (14 cm) = 112/3 cm³.
Hence, the maximum volume of the square pyramid that can fit inside a cube with a side length of 14 cm is approximately 149.33 cm³.