Shining a torch perpendicular on a paper makes a circular spot. If you tilt the paper, the circle is converted to an ellipse and the area of the spot increases. How much does the area increase if we tilt the paper by 23 degrees?
Answers
Given : Shining a torch perpendicular on a paper makes a circular spot. If you tilt the paper, the circle is converted to an ellipse and the area of the spot increases.
To find : How much does the area increase if we tilt the paper by 23 degrees?
Solution:
Let say Circle radius is r and center is origin
x² + y² = r²
Area of circle = πr²
Paper is tilted at 23° from x axis in z direction
Y axis remain unchanged
z axis coordinate will be x tan23°
hence ellipse area would be
Distance of rtan23° from center
= √r² + (rtan23°)²
= √r²(1 + tan²23°)
= √r²sec²23°)
= rsec23°
Area of ellipse = πab
= πrrsec23
= πr²sec23°
% increase in area = 100 * ( πr²sec23° - πr²)/πr²
= 100 ( Sec23° - 1)
= 100 (0.08636)
= 8.636%
8.636% area increased
Learn more:
Find the equation for the ellipse that satisfies the given conditions ...
https://brainly.in/question/17176084
Area of the greatest rectangle inscribed in the ellipse - Brainly.in
https://brainly.in/question/14037484
