233k views
4 votes
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

User Memtha
by
7.7k points

2 Answers

2 votes

Answer:

Option B is correct.

The estimated perimeter of an ellipse is 37.3ft

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{(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{(\left (7.5\right )^2+\left (3.75\right )^2)/(2)}


P\approx 2\cdot 3.14\cdot \sqrt{(56.25+14.0625)/(2)}


P\approx\ 6.28\cdot \sqrt{(70.3125)/(2)}


P\approx\ 6.28\cdot √(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.
















User Teo Choong Ping
by
8.0k points
7 votes

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

User James Iry
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories