A holiday ornament in the shape of a square pyramid has the following dimensions: 2.75 times 2.75 in. What is the approximate volume of the ornament. Round your answer to the nearest hundredth.
24.47 in
9.01in
6.93in
20.80 in
The volume of a square pyramid is given by the formula V = (1/3) * base area * height.
First, we need to find the base area, which is the area of a square with sides measuring 2.75 in. The formula for the area of a square is A = s^2, where s is the side length.
Base area = 2.75^2 = 7.5625 sq in
Now we need to find the height of the pyramid. The height is the distance from the center of the base to the apex of the pyramid. Since the pyramid is a square pyramid, the height can be found using the Pythagorean theorem.
The diagonal of the base is the height and it can be found using the formula a^2 + b^2 = c^2, where a and b are the base sides and c is the diagonal.
2.75^2 + 2.75^2 = c^2
2 * 2.75^2 = c^2
c = sqrt(2 * 2.75^2) ≈ 3.887 in
Now we have both the base area and height, we can calculate the volume of the square pyramid:
V = (1/3) * 7.5625 * 3.887 ≈ 9.61 cubic inches
So, the approximate volume of the holiday ornament in the shape of a square pyramid is 9.61 cubic inches. Rounding to the nearest hundredth gives 9.61 in.