Question

What is the estimated perimeter of an ellipse if the major axis has a length of 15 ft and the minor axis has a length of 7.5 ft? Round your answer to the nearest tenth. A. 36.7 ft B. 37.3 ft C. 25.7 ft D. 24.2 ft

Answer 1

Answer:

Option B is correct.

The estimated perimeter of an ellipse is 37.3ft

Step-by-step explanation:

Given:

Length of Major-axis (2a)=15ft

Length of minor-axis (2b)=7.5ft

For an ellipse, the perimeter (P) approximately given by:

$P\approx 2\pi\sqrt{\frac{a^2+b^2}{2}}$ , where a and b are semi major axis and semi minor axis respectively.(Use approx. value of $\pi =3.1 4$)

Here, a=7.5ft and b=3.75ft,  putting in above equation, we get

$P\approx 2\pi\sqrt{\frac{\left (7.5\right )^2+\left (3.75\right )^2}{2}}$

$P\approx 2\cdot 3.14\cdot \sqrt{\frac{56.25+14.0625}{2}}$

$P\approx\ 6.28\cdot \sqrt{\frac{70.3125}{2}}$

$P\approx\ 6.28\cdot \sqrt{35.15625}$

After solving the square-root we get,

$P\approx\ 6.28\cdot5.92927061$

$P\approx37.3ft$.

Therefore, the estimated perimeter of an ellipse is 37.3ft.

Answer 2

P = 2*pi*sqrt(a^2 +b^2/2 =

2 *3.14 * sqrt(15/2^2 +7.5/2^2/2 =

6.28 x sqrt(56.25+14.0625/2

6.28 *sqrt(35.15625)

6.28 * 5.929270613= 37.235

answer is B 37.3 feet