Tag: how many squares

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Questions Related to how many squares

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

The side of a square is 2 cm Semicircles are constructed on two sides of the square then the area of the whole figure is

  1. $ \displaystyle (4+\pi )cm^{2} $
  2. $ \displaystyle (4+4\pi )cm^{2} $
  3. $ \displaystyle 4\pi cm^{2} $
  4. $ \displaystyle 8\pi cm^{2} $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The side of square is 2 cm 

Then area of square =$(2)^{2}=4 cm^{2}$
The Semicircle constructed on two side diameter 2 cm then radius =1 cm
Then area of one semicircle =$\frac{\pi r^{2}}{2}=\frac{\pi (1)^{2}}{2}=\frac{\pi }{2}$
Then  area of two semicircle=$2\times \frac{\pi }{2}=\pi $
So total area of whole figure=$(4+\pi )cm^{2}$

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

A square of side x is taken A rectangle is cut out from this square such that one side of the rectangle is half that of the square and the other is $\displaystyle \frac{1}{3}$ of the first side of the rectangle
What is the area of the remaining portion?

  1. $\displaystyle \left ( \frac{3}{4} \right )x^{2}$
  2. $\displaystyle \left ( \frac{7}{8} \right )x^{2}$
  3. $\displaystyle \left ( \frac{11}{12} \right )x^{2}$
  4. $\displaystyle \left ( \frac{15}{16} \right )x^{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the side of square is x 

Then area of square=$x^{2}$
Given one side of rectangle is half of square=$\frac{x}{2}$
And second side is $\frac{1}{3}$ of other side=$\frac{1}{3}\times \frac{x}{2}=\frac{x}{6}$
Then area of rectangle =$\frac{x}{2}\times \frac{x}{6}=\frac{(x)^{2}}{12}$
So remaining area of square =$x^{2}-\frac{(x)^{2}}{12}=\frac{11x^{2}}{12}$

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

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?

  1. xy and 2xy + 2yz

  2. xy and 2xz + 2yz

  3. xy and 2xy

  4. xy and 2xy + 2xz
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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

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

  1. 75

  2. 100

  3. 125

  4. 150
Reveal answer Fill a bubble to check yourself
B Correct answer
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

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

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

  1. $8$ square inches
  2. $10$ square inches
  3. $6$ square inches
  4. $9$ square inches
Reveal answer Fill a bubble to check yourself
D Correct answer
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.