I'm here to help you with the problem provided. Let's solve it step by step:
1. **Finding the Length of the Slant Height:**
- Given: height of the frustum = 14 cm, area of the larger base = 256 cm², and angle between the smaller base and the slant height = 115°.
- To find the length of the slant height, we can use trigonometry. Since the frustum is a square pyramid, we can consider the right triangle formed by the slant height, the height, and half the diagonal of the larger base.
- We can use the formula: sin(angle) = opposite/hypotenuse, where sin(115°) = 14/hypotenuse.
- Solving for the hypotenuse (slant height) gives us the length of the slant height.
2. **Finding the Volume of the Frustum:**
- The volume of a frustum of a pyramid can be calculated using the formula: V = (1/3) * π * h * (r₁² + r₂² + r₁ * r₂), where h is the height of the frustum, r₁ is the radius of the larger base, and r₂ is the radius of the smaller base.
- In this case, since the bases are squares, the radius of each base is half the length of its diagonal.
- Once you have the length of the slant height from the previous step, you can find the radii of the bases and then calculate the volume of the frustum using the given formula.
Remember to round your answers to the nearest appropriate unit as requested in the question. If you have any more questions or need further clarification, feel free to ask!
