The surface area of an ellipsoid cap can be approximated using the formula:

$S \approx 2\pi a b \left(1 - \frac{c - h}{c} \right)^{p}$

where

• $a, b, c$ are the semi-axes of the ellipsoid,
• $h$ is the cap height,
• $p$ is an exponent given by $p \approx 1.6075$ for better accuracy.

Given values:

• $a = 8$,
• $b = 6$,
• $c = 5$,
• $h = 3$.

Now, we substitute these values and compute the surface area. Let me calculate it. math

Given values

a = 8 b = 6 c = 5 h = 3 p = 1.6075 # Empirical exponent for better accuracy

Compute the surface area of the ellipsoid cap

S = 2 * math.pi * a * b * ((1 - (c - h) / c) ** p) SThe surface area of the ellipsoid cap is approximately 132.68 square units.

Would you like a step-by-step breakdown of the calculation?

Related Questions:

1. How do you derive the formula for the surface area of an ellipsoid cap?
2. What is the volume of the ellipsoid cap given the same parameters?
3. How does changing $h$ affect the surface area of the cap?
4. How is the surface area of a spherical cap different from an ellipsoid cap?
5. Can we derive an exact formula for the surface area instead of an approximation?

Tip:

For a more accurate calculation, numerical integration methods can be used to determine the exact surface area of an ellipsoid cap.