Question

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Answer 1

Answer:

Correct Question -

The circumference of two circle are in the ratio 2 : 3. Find the ratio of their areas.

Given -

Ratio of their circumference = 2:3

To find -

Ratio of their areas.

Formula used -

Circumference of circle

Area of circle.

Solution -

In the question, we are provided, with the ratios of the circumference of 2 circles, and we need to find the ratio of area of those circle, for that first we will use the formula of circumference of a circle, then we will use the formula of area of circles. We will be writing 1 equation in it too.

So -

Let the circumference of 2 circles be c1 and c2

According to question -

c1 : c2

Circumference of circle = 2πr

where -

π = $\tt\dfrac{22}{7}$

r = radius

On substituting the values -

c1 : c2 = 2 : 3

2πr1 : 2πr2 = 2 : 3

$\tt\dfrac{2\pi\:r\:1}{2\pi\:r\:2}$ = $\tt\dfrac{2}{3}$

$\tt\dfrac{r1}{r2}$ = $\tt\dfrac{2}{3}$$\longrightarrow$ [Equation 1]

Now -

Let the areas of both the circles be A1 and A2

Area of circle = πr²

So -

Area of both circles = πr1² : πr2²

On substituting the values -

A1 : A2 = πr1² : πr2²

$\tt\dfrac{A1}{A2}$ = $\tt\dfrac{(\pi\:r1)}{(\pi\:r2)}^{2}$

$\tt\dfrac{A1}{A2}$ = $\tt\dfrac{(r1)}{(r2)}^{2}$

$\tt\dfrac{A1}{A2}$ = $\tt\dfrac{(2)}{(3)}^{2}$ [From equation 1]

So -

$\tt\dfrac{A1}{A2}$ = $\tt\dfrac{4}{9}$

$\therefore$ The ratio of their areas is 4 : 9

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Answer 2

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Concept}}}$

Here the concept of Area of Rectangle and Area of Square has been used. We see that se are given the dimensions of rectangular room abd squared tile. Now firstly we shall find the area of the rectangular room using the formula of area of rectangle this is because only floor of the room is covered with tiles. Then we will find the area of squared tile using the formula of area of square. Also, the sum of areas of required tile will be equal to the area of room. So using this concept we can find our answer.

Let's do it !!

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★ Formula Used :-

$\\\;\boxed{\sf{\pink{Area\;of\;Rectangle\;=\;\bf{Length\:\times\:Breadth}}}}$

$\\\;\boxed{\sf{\pink{Area\;of\;Square\;=\;\bf{(Side)^{2}}}}}$

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★ Solution :-

Given,

» Dimensions of the room = Length × Breadth = 6 m × 8 m = 600 cm × 800 cm

(since 1 m = 100 cm)

» Dimension of the square tiles = Side = 40 cm

* Here we have converted the values in same unit to get the correct answer.

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~ For the Area of Rectangular Room ::

We know that,

$\\\;\sf{\rightarrow\;\;Area\;of\;Rectangle\;=\;\bf{Length\:\times\:Breadth}}$

By applying values we get,

$\\\;\sf{\Longrightarrow\;\;Area\;of\;Rectangular\;Room\;=\;\bf{600\:\times\:800}}$

$\\\;\bf{\Longrightarrow\;\;Area\;of\;Rectangular\;Room\;=\;\bf{\red{480000\;\;cm^{2}}}}$

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~ For the Area of each square tile ::

We know that,

$\\\;\sf{\rightarrow\;\;Area\;of\;Square\;=\;\bf{(Side)^{2}}}$

By applying values, we get

$\\\;\sf{\rightarrow\;\;Area\;of\;Square\;Tiles\;=\;\bf{(40)^{2}}}$

$\\\;\bf{\rightarrow\;\;Area\;of\;Square\;Tiles\;=\;\bf{\blue{1600\;\;cm^{2}}}}$

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~ For the number of square tiles required ::

We can calculate this from the following relationship,

$\\\;\bf{\orange{\mapsto\;\;No.\;of\;tiles\;required\;=\;\bf{\dfrac{\red{Area\;of\;Room}}{\blue{Area\;of\;each\;Tile}}}}}$

Now by applying values, we get

$\\\;\sf{\mapsto\;\;No.\;of\;tiles\;required\;=\;\bf{\dfrac{480000}{1600}}}$

By cancelling zeroes, we get

$\\\;\sf{\mapsto\;\;No.\;of\;tiles\;required\;=\;\bf{\dfrac{4800}{16}}}$

$\\\;\bf{\mapsto\;\;No.\;of\;tiles\;required\;=\;\bf{\green{300\;Tiles}}}$

$\\\;\underline{\boxed{\tt{Hence,\;\:no.\;of\;\:tiles\;\:required\;=\;\bf{\purple{300\;\:Tiles}}}}}$

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★ More to know :-

$\\\;\sf{\leadsto\;\;Perimeter\;of\;Rectangle\;=\;2(Length\:+\:Breadth)}$

$\\\;\sf{\leadsto\;\;Perimeter\;of\;Square\;=\;4\:\times\:Side}$

$\\\;\sf{\leadsto\;\;Diagonal\;of\;Rectangle\;=\;\sqrt{(L^{2}\:+\:B^{2})}}$

$\\\;\sf{\leadsto\;\;Diagonal\;of\;Square\;=\;Side\sqrt{2}}$

• Rectangle is a type of parallelogram whose opposite sides are equal and parallel.

• Square is a type of parallelogram whose all the sides are equal.

• All the angles of rectangle and square equal to 90°

• Diagonals of the square and rectangle bisect each other.