Question

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.​

Answer 1

Answer:

Step-by-step explanation:

lets say radius of circle =r

AB = 2r+2r+r=5r

AD=2r

area of card board= l X b = 2r X 5r = $10r^{2}$

area of two circle and one semicircle = $2*\pi r^{2}+\frac{1}{2}\pi r^{2} =(2+\frac{1}{2} )\pi r^{2}=\frac{5}{2} \pi r^{2}$$=\frac{5}{2} *\frac{22}{7} r^{2}=\frac{55}{7} r^{2}$

area of remaining cardboard = area of card board - area of two circle and one semicircle

area of remaining cardboard = $10r^{2}$ - $\frac{55}{7} r^{2}$ =  $(10-\frac{55}{7} ) r^{2} = (\frac{70-55}{7} )r^{2}=\frac{15}{7} r^{2}$

$\frac{area of remaining cardboard}{area of card board} =$ $\frac{\frac{15}{7} r^{2}}{8r^{2}}=\frac{15}{56}$

Answer 2

ANSWER:

Given:

• 2 circles and a semi circle is cut from a rectangular cardboard.

To Find:

• Ratio of area of remaining cardboard and area of cardboard.

Solution:

Let the radius of the semi circle and the 2 circles be x cm.

So, we can see that,

⇒ AD = BC = diameter(circle) = 2x

And,

⇒ AB = CD = x + 2x + 2x = 5x

Now, we will find the area of the 2 circles and the semi circle.

So,

⇒ Area of circle = πr²

⇒ Area of 2 circles and 1 semicircle = (πr²) + (πr²) + (πr²/2)

⇒ Area of 2 circles and 1 semicircle = 5/2 × πr²

⇒ Area of 2 circles and 1 semicircle = 5/2 × πx² ---(1)

Now, we will find the area of the rectangle.

So,

⇒ Area of rectangle = length × breadth

⇒ Area of rectangle ABCD = AB × CD

As, AB = 5x and BC = 2x.

So,

⇒ Area of rectangle ABCD = 5x × 2x

⇒ Area of rectangle ABCD = 10x² ----(2)

At last, we will find the area of cardboard left after cutting out the circles and semicircle.

⇒ Area of remaining cardboard = Area of cardboard - Area of circles and semicircle

⇒ Area of remaining cardboard = 10x² - (5πx²)/2

⇒ Area of remaining cardboard = 5x²(4 - π)/2 ----(3)

We need to find,

⇒ Ratio of area of remaining cardboard and area of cardboard

⇒ Ratio = (Area of remaining cardboard)/(Area of cardboard)

From (2) and (3),

⇒ Ratio = [5x²(4 - π)/2] ÷ [10x²]

⇒ Ratio = 5x²(4 - π)/20x²

⇒ Ratio = 4 - π/4

Putting π = 22/7,

⇒ Ratio = 4 - (22/7)/4

⇒ Ratio = [(28 - 22)/7]/4

⇒ Ratio = 6/28

⇒ Ratio = 3/14

⇒ Ratio = 3 : 14

Hence, the ratio between the area of the remaining cardboard and area of cardboard is 3 : 14