Question for Only:- ❏ Moderators ❏ Brainly Stars ❏ Best users ✰ QUESTION ✰from a rectangular cardboard ABCD 2 circles and 1 semicircle of a largest side are cut. calculate the ratio between the area of the remaining cardboard and area of cardboard.
Answers
Answer:
(1 - π/4) : 1 or (π - 4):4 or 3 : 14
Step-by-step explanation:
let the radii of the circle(s) be 'r'.
Observing the figure, we get:
Breadth of rect. = r + r = 2r
Length of rect. = r + 2r + 2r = 5r
∴ Initially:
Area of rect. = l * b
= 5r * 2r
= 10r²
When the area of 2 circle and semi-cricle is cut:
⇒ Remaining area = Area of rectangle - [2ar. of circle + ar. of semi-circle + ar. of semi-circle]
⇒ Remaining area = 10r² - [2*πr² + 1/2 πr²]
= 10r² - (5/2)πr²
= 10r²[1 - π/4]
∴ Required ratio = 10r²(1 - π/4) : 10r²
= (1 - π/4) : 1
Or, = (4 - π) : 4
Required Ratio = 10r²(1 - π/4) : 10r²
= (1-π/4) : 1
= (4 - π) : 4