84.1k views
5 votes
PLEASE HELP!!!! The base of a 6 cm tall circular cone is inscribed in the base of a 12 cm tall square pyramid with base edges of 4 cm. What is the volume of the space between the cone and pyramid?

User Zutty
by
7.7k points

1 Answer

5 votes

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.

User Felix Seele
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.