Tag: maths

Questions Related to maths

Area bounded by $y|y|-x|x|=1,\ y|y|+x|x|=1$ and $y=|x|$ is

maths how many squares area of rectangular paths comparing areas spaces and boundaries - 2

  1. $\dfrac{\pi}{2}$

  2. ${\pi}$

  3. $\dfrac{\pi}{4}$

  4. $None\ of\ these$

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Correct Option: A

A farmer wishes to cultivate four different crops in equal areas in his $1$ car of land.. The land he should allocate for each crop is:  

maths how many squares area of rectangular paths comparing areas spaces and boundaries - 2

  1. $10\ m^{2}$

  2. $25\ m^{2}$

  3. $75\ m^{2}$

  4. $100\ m^{2}$

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Correct Option: A

A room is x meters long, y meters broad, and z meters high; find how many square meters of carpet will be required for the floor and how many square meters of paper for the walls?

maths how many squares area of rectangular paths comparing areas spaces and boundaries - 2

  1. xy and 2xy + 2yz

  2. xy and 2xz + 2yz

  3. xy and 2xy

  4. xy and 2xy + 2xz

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Correct Option: B
Explanation:

$Length = x, breadth = y$
Area of the floor $= xy m^2$
Area of four walls $= 2h(l + b) = 2z (x +y) = 2zx + 2yz$

Find the area of a square inscribed in a circle of radius $\displaystyle 5\sqrt{2}$ cm (in $\displaystyle cm^{2}$)

maths how many squares area of rectangular paths comparing areas spaces and boundaries - 2

  1. 75

  2. 100

  3. 125

  4. 150

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Correct Option: B
Explanation:

The diagonal of the square will be equal to the diameter of the circle.
So,diagonal of the square $ = 2 \times 5 \sqrt {2} = 10 \sqrt {2} $

Diagonal of a square $ = \sqrt {2} \times side $
So, $ 10 \sqrt {2} = \sqrt {2} \times side $
$ => Side  =  10  cm $

Area of the square $ = { side }^{ 2 } = { 10 }^{ 2 } = 100 $ sq cm

What is the maximum area of a four-sided plane with a perimeter of $12$ inches?

maths how many squares area of rectangular paths comparing areas spaces and boundaries - 2

  1. $8$ square inches

  2. $10$ square inches

  3. $6$ square inches

  4. $9$ square inches

Show answer
Correct Option: D
Explanation:

The area is maximum when the four-sided plane is a square.

The perimeter of a square $ = 4 \times$ side $= 12 $ inches
$ \Rightarrow$ side $= 3  $ inches

Now, area of the square $ =$ side $\times$ side $= 3 \times 3 = 9 $ square inches.

Calculate area of the shape obtained by joining an equilateral triangle to one of the end of rectangle and a semicircle to the other end of rectangle. The sides of equilateral triangle is $3$ cm and one of the sides of rectangle is $4$ cm.

maths how many squares area of rectangular paths comparing areas spaces and boundaries - 2

  1. $28.12\ cm^{2}$

  2. $30.02\ cm^{2}$

  3. $35.02\ cm^{2}$

  4. $40.02\ cm^{2}$

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Correct Option: B

Consider a rectangle of perimeter $24\ cm$ with sides $a$ and $b$. Then the total number of square grids formed in that rectangle is given by

maths spaces and boundaries - 2 area of rectangular paths comparing areas problems on areas

  1. $a\times b$

  2. $a+b$

  3. $a-b$

  4. $\dfrac{a}{b}$

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Correct Option: A
Explanation:
Area of rectangle$=a\times b$
Area of $1$ square grid$=1 cm^2$
No. of square grids$=\cfrac { a\times b }{ 1 } =a\times b$

Form a rectangle with $8$ square grids where each square grid measure $1\ cm^{2}$. Find the total area of the rectangle.

maths spaces and boundaries - 2 area of rectangular paths comparing areas problems on areas

  1. $8\ cm^{2}$

  2. $12\ cm^{2}$

  3. $16\ cm^{2}$

  4. $20\ cm^{2}$

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Correct Option: A
Explanation:

Area of rectangle$=8\times $ area of $1$ square grid$=8\times 1=8 cm^2$

Let there be a rectangle of area $24\ cm^{2}$. Then find the total number of square grids made in this rectangle.(Each square grid measures $1\ cm^{2}$)

maths spaces and boundaries - 2 area of rectangular paths comparing areas problems on areas

  1. $3$

  2. $6$

  3. $12$

  4. $24$

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Correct Option: D
Explanation:

Number of square grids$=\cfrac { Area\quad of\quad rectangle }{ area\quad of\quad square\quad grid } =\cfrac { 24 }{ 1 } =24$

Three coins of the same size (radius $1cm$) are placed on table such that each of them touches the other two. The area enclosed by the coins is:

maths spaces and boundaries - 1 area of rectangular paths comparing areas spaces and boundaries - 2

  1. $\left( \cfrac { \pi }{ 2 } -\sqrt { 3 } \right) { cm }^{ 2 }$

  2. $\left( \sqrt { 3 } -\cfrac { \pi }{ 2 } \right) { cm }^{ 2 }$

  3. $\left(2 \sqrt { 3 } -\cfrac { \pi }{ 2 } \right) { cm }^{ 2 }$

  4. $\left(3 \sqrt { 3 } -\cfrac { \pi }{ 2 } \right) { cm }^{ 2 }$

Show answer
Correct Option: B
Explanation:

Radius of each coin $=1\ cm$

With all the three centres an equilateral triangle of side 2 cm is formed.
Area enclosed by coind $=$ Area of equilateral triangle $-3\times$ Area of sector of angle $60^{o}$
                                         $=\dfrac{\sqrt3}{2}(2)^2-3\times\dfrac{60}{360}\times\pi(1)^2$
                                         $=\dfrac{\sqrt3}{4}\times4-3\times\dfrac{1}{6}\times\pi$
                                          $=\left(\sqrt3-\dfrac{\pi}{2}\right)\ cm^2$