A square pyramid with a base length of 5 and a height of 10 is placed vertically inside a cube with a base length of 5. What is the volume of the square pyramid inside the cube?

To find the volume of the square pyramid placed inside the cube, let's go step by step:

### Step 1: Formula for the Volume of a Square Pyramid
The volume \( V \) of a square pyramid can be calculated using the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]

### Step 2: Calculate the Base Area of the Square Pyramid
The base of the square pyramid is a square with side length 5 units (since the base length of both the cube and the pyramid is 5 units).
\[
\text{Base Area} = 5 \times 5 = 25 \, \text{square units}
\]

### Step 3: Height of the Pyramid
The given height of the pyramid is 10 units.

### Step 4: Calculate the Volume
Now, substitute the base area and height into the formula for the volume of the pyramid:
\[
V = \frac{1}{3} \times 25 \times 10 = \frac{1}{3} \times 250 = \frac{250}{3} \approx 83.33 \, \text{cubic units}
\]

### Final Answer:
The volume of the square pyramid inside the cube is approximately \( 83.33 \, \text{cubic units} \).

Would you like further details on any step?

Here are some related questions:
1. How do you find the volume of the cube?
2. What is the surface area of the pyramid?
3. How does the volume of a pyramid compare to a cube with the same base area and height?
4. How would the volume change if the base length of the pyramid were doubled?
5. How can you find the slant height of the pyramid?

**Tip:** The volume of a pyramid is always one-third of the volume of a prism with the same base and height.

Learn how to calculate the volume of a square pyramid with a base length of 5 and height of 10 inside a cube. This problem explores geometry concepts such as the volume formula for pyramids and is suitable for students in Grades 7-9.

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