Question

A tent in the shape of a square pyramid has a volume of 6.25 cubic meters. The height of the tent is 3 meters. What is the edge length of the base of the tent?

Answer 1

To find the edge length of the base of the tent, we calculate the area of the base and then find the length of one side of the square. The area of the base is 6.25 square meters and the length of one side is approximately 2.5 meters.

Step-by-step explanation:

To find the edge length of the base of the tent, we need to calculate the area of the base and then find the length of one side of the square. The formula for the volume of a square pyramid is V = (1/3) * B * h, where V is the volume, B is the area of the base, and h is the height. Given that the volume is 6.25 cubic meters and the height is 3 meters, we can rearrange the formula to solve for B: B = (3 * V) / h. Plugging in the values, we get B = (3 * 6.25) / 3 = 6.25 square meters.

The area of a square is given by the formula A = s^2, where A is the area and s is the length of one side. Therefore, s = √A. Taking the square root of 6.25, we find that s is approximately 2.5 meters.

Answer 2

To find the edge length of the base of the tent, we use the volume formula for a pyramid, plug in the given values, and solve for the side length 'a'. After the calculations, we find that the edge length of the base of the tent is 2.5 meters.

Step-by-step explanation:

To determine the edge length of the base of a tent that is in the shape of a square pyramid, we can use the formula for the volume of a pyramid, which is V = (1/3) * base area * height. Since the volume is given as 6.25 cubic meters and the height is 3 meters, we can set up the following equation:

V = (1/3) * a² * h where a is the side length of the square base and h is the height of the pyramid.

Plugging in the values we get:

6.25 m³ = (1/3) * a² * 3 m

Dividing both sides by 3 meters, we get:

2.0833... m² = (1/3) * a²

Multiplying both sides by 3, we obtain:

6.25 m² = a²

Finally, taking the square root of both sides:

a = √6.25 m²

a = 2.5 meters

Thus, the edge length of the base of the tent is 2.5 meters.