Answer:
Explanation:
To find the volume of the space between the cone and pyramid, we need to calculate the volumes of both shapes and then subtract them.
Let's start with the cone:
The height of the cone is given as 6 cm, and the radius can be determined by half of the side length of the square base of the pyramid (4 cm). So the radius of the cone is 2 cm.
The formula for the volume of a cone is given by V_cone = (1/3) * π * r^2 * h, where r is the radius and h is the height.
Plugging in the values, we get:
V_cone = (1/3) * π * 2^2 * 6
= (1/3) * π * 4 * 6
= 8π cm³
Next, let's calculate the volume of the square pyramid:
The height of the square pyramid is given as 12 cm, and the base edges are 4 cm.
The formula for the volume of a square pyramid is given by V_pyramid = (1/3) * base area * height.
The base area of a square is given by side length squared, so the base area of the pyramid is 4^2 = 16 cm².
Plugging in the values, we get:
V_pyramid = (1/3) * 16 * 12
= 64 cm³
Now, we can find the volume of the space between the cone and pyramid by subtracting the volume of the cone from the volume of the pyramid:
V_space = V_pyramid - V_cone
= 64 - 8π
≈ 36.849 cm³ (rounded to three decimal places)
Therefore, the volume of the space between the cone and pyramid is approximately 36.849 cm³.