MCQ Questions for Class 6 Maths Mensuration Quiz 3

Jen wants to tile the floor of her kitchen. The floor is rectangular and measures

$12$ feet by

$8$ feet. If it costs

$\text{Rs. }2.50$ per square foot for the materials, what is the total cost of the materials for tiling the kitchen floor?

0%
$\text{Rs. }160$
0%
$\text{Rs. }200$
0%
$\text{Rs. }220$
0%
$\text{Rs. }240$

Explanation

The given floor is rectangular with length

$(l)=12$ feet and breadth

$(b)=8$ feet

Area of the rectangular floor

$=l\times b$

$=12\times 8$

$=96$ sq. feet

Given

$\text{Rs. } 2.50$ is the cost of the materials per square foot.

$\therefore$ Cost of materials for

$96$ sq. feet

$=96\times 2.50$

$=\text{Rs. }240.0$

An athlete takes 15 rounds & a rectangular park, 30 m long and 20 m wide. The total distance covered by him is ________.

0%
$1500$ m
0%
$1300$ m
0%
$1200$ m
0%
$1550$ m

Explanation

Length of rectangular park = 30 m
Breadth of rectangular park = 20 m

$\therefore$ Perimeter of park = 2(30 20) = 100 m
So, distance covered by the athlete in 15 rounds =

$15 \times 100 = 1500 m$

Calculate area of the figure made by joining

$25$ unit squares.

0%
$22$ sq. unit
0%
$23$ sq. unit
0%
$24$ sq. unit
0%
$25$ sq. unit

Explanation

Area of figure

$=25\times 1=25$ sq. unit

Parul walks twice around a square field of side

$25$ m. Nitish walks thrice around a rectangular field with length

$20$ m and breadth

$14$ m. Who covers more distance and by how much?

0%
Nitish, $4$ m
0%
Parul, $6$ m
0%
Nitish, $204$ m
0%
Parul, $8$ m

Explanation

We know that, distance covered by Parul is twice the perimeter of Square

and Distance covered by Nitish is thrice the perimeter of rectangle.

Perimeter of Square

$=4\times \text{Side}$

$= 4\times 25 =100 \text{ m}$

Perimeter of Rectangle

$=2(\text{Length}+ \text{Breadth})$

$= 2(20+14)= 68 \text{ m}$

Therefore, distance covered by Parul

$=2\times 100= 200 \text{ m}$

And Distance covered by Nitish

$=3\times 68 = 204 \text{ m}$

Hence, Nitish Travels more distance by

$4 \text{ m}$

Each square in the figure covers an area of

$2$ in

$^{2}$ . What is the area of the region enclosed in the figure shown?

0%
$42\ in^{2}$
0%
$48\ in^{2}$
0%
$56\ in^{2}$
0%
$64\ in^{2}$

Explanation

Number of squares enclosed

$=21$

Area of figure

$21\times 2=42$ square units.

Calculate the perimeter of the following figures:

0%
(1) $18a$
(2) $11b$
0%
(1) $10a$
(2) $44b$
0%
(1) $20a$
(2) $22b$
0%
none

Latika wants to put a border around her bedsheet of length 10 m and breadth 5 m 60 cm. Find the total cost of the border required at the rate of Rs 90 per metre.

0%
$Rs\ 2808$
0%
$Rs\ 2505$
0%
$Rs\ 2408$
0%
$Rs\ 2605$

Explanation

Length of bedsheet

$= 10 m$
Breadth of bedsheet

$= 5 m\ 60 cm = 5.6 m$ (as

$1m=100cm$ )
Perimeter of bedsheet

$= 2(10 + 5.6)$

$=2 \times (15.6) = 31.2 m$
Cost of

$1 m$ border

$= Rs 90$

$\therefore$ Total cost

$=$ Rs

$(90 \times 31.2) = Rs\ 2808$

Calculate the approximate area enclosed in the figure if the area of each square is

$6\text{ sq. units}.$

0%
$180\text{ sq. units}$
0%
$252\text{ sq. units}$
0%
$270\text{ sq. units}$
0%
$288\text{ sq. units}$

Explanation

The number of squares enclosed in the given figure is equal to

$45.$ It is given that area of each square is equal to

$6\text{ sq. units}.$

Area of figure,

$A=45\times 6$

$=270\text{ sq. units}$

Estimate the area of the shaded region. Each unit is

$1$ square inch.

0%
$14$ sq. in
0%
$22$ sq. in
0%
$30$ sq. in
0%
$38$ sq. in

Explanation

Number of full squares

$=18$

Number of half squares

$=8$

Area of figure

$=18\times 1+8\times \cfrac { 1 }{ 2 } =22 \text{ sq. in}$

The length and breadth of a rectangular field are

$260m$ and

$130m$ respectively, then its area is ______ .

0%
$338$
0%
$3380$
0%
$3800$
0%
$33800$

Explanation

$\Rightarrow$ Here, length and breadth of rectangular field is

$260\,m$ and

$130\,m$ .

$\Rightarrow$ Area of rectangular field =

$length \times breadth$

$\therefore$ Area of rectangle =

$260\,m\times 130\,m=33800\,m^2$

A figure is formed by putting two squares one on the other as shown in the figure. If the length of each side of the two squares is

$8cm$ , then the perimeter of the figure formed is ________ .

0%
$56cm$
0%
$64cm$
0%
$32cm$
0%
$48cm$

Explanation

$\Rightarrow$

$ABCF$ and

$FCDE$ are two squares.

Length of each side of square is

$8\,cm$ .

$\Rightarrow$ Perimeter of ABCD

$=$

$AB+BC+CD+DE+EF+FA$

$\Rightarrow$ Perimeter of ABCD

$=$

$8 + 8 + 8 + 8 + 8 + 8$

$\therefore$ Perimeter of ABCD

$=$

$48 cm.$

What is the perimeter of a rectangle with length

$=4\ cm$ and breadth

$=2\ cm$ ?

0%
$6\ cm$
0%
$12\ cm$
0%
$32\ cm^{2}$
0%
$8\ cm^{2}$

Explanation

The perimeter of a rectangle is

$2(l+b)$

The measurements of given rectangle are

$l=4cm,\ b=2cm$

Perimeter of Given rectangle

$=2(4+2)cm$

$=12cm$

The perimeter of the rectangle whose length is

$24\ cm$ and the diagonal is

$30\ cm$ is:

0%
$84\ cm$
0%
$42\ cm$
0%
$54\ cm$
0%
$108\ cm$

Explanation

Length of rectangle $(l)$ is 24 cm.

Length of diagonal $(d)$ is 30 cm.

Let the length of breadth be $b$ .

Write the formula to calculate the diagonal of rectangle.

$d=\sqrt{b^{2}+h^{2}}$ (1)

Substitute the values in equation (1).

$30 = \sqrt{b^{2}+\left ( 24 \right )^{2}}$

Solve for $b$ .

$b^{2}=900-576$

$b^{2}=324$

$b=\pm 18$

Since the breath cannot be negative. So, neglect the negative value of breadth. Hence, the breadth of the rectangle is $18$ cm.

Write the formula to calculate perimeter of rectangle.

$P=2\left ( l+b \right )$ (2)

Substitute the values in equation (2).

$P=2\left ( 24+18 \right )$

$=2\left ( 42 \right )$

$=84$

Thus, the perimeter of rectangle is $84$ cm.

Find the perimeter of a square of length

$25 \,cm$ .

0%
$625$ cm
0%
$100$ cm
0%
$125$ cm
0%
$25$ cm

Explanation

We have the perimeter of a square

$=4\times side$

therefore the perimeter of a square of length

$25$ cm is

$=4\times 25=100$ cm.

(distance between two dots is 1 cm)

12 Red square can fit inside

$Green \,Rectangle \,A$

12 Red square can fit inside

$Green \,Rectangle \,B$

Which Rectangle has smaller perimeter

0%
Green Rectangle B
0%
Green Rectangle A
0%
Both A and B have equal perimeter
0%
Can not be determined

If the perimeter of a rectangular field is 200 m add its breadth is 40 m then its area is (in

$m^2$ ):

0%
1200
0%
2400
0%
4800
0%
6000

Explanation

Perimeter of the rectangular field

$=2(l+b)$

where l and b are the length and breadth of the rectangular field

$\Rightarrow 200=2(l+40)$

$\Rightarrow l+40=100$

$\Rightarrow l=60\ m$

Area of the rectangular field

$=lb$

$=60\times40$

$=2400\ m^2$

The length of a garden is

$200$ m and its area is

$3$ hectares

$20$ ares. What is the breadth of the garden?

0%
$320$ m
0%
$240$ m
0%
$180$ m
0%
$160$ m

The length of a rectangle is

$9$ cm and its breadth is

$y$ cm. Its perimeter (in cm) is

0%
$(y+9)+2$
0%
$2\times (y+9)$
0%
$2y+9$
0%
$y+18$

To find the cost of painting a wall we need to find the perimeter of the wall.

0%
True
0%
False

Explanation

To find the cost of painting a wall we need to find area of the wall and not perimeter because if we would paint the area of wall and not the borders of the wall
Hence, to find the cost of painting we should require the area of wall.

$\textbf{So, the given statement is false.}$

If the length of a rectangle is halved and breadth is doubled then the area of the rectangle obtained remains the same.

0%
True
0%
False

Explanation

Area of square

$=(side)^2$

$=(s)^2$

New side of square

$= 2s$
Area of new square

$= (2s) \times (2s)$

$=(4s)^2$
Thus, area becomes four times if side of a square becomes double.

$\textbf{So, the given statement is false.}$

Area of a square is doubled if the side of the square is doubled.

0%
True
0%
False

Explanation

Let, the side of the original square be

$a$

Then, the side of new square be

$=2a$

Now

Area of the original square

$= a^{2}$

And, area of new square

$= (2a)^{2} = 4a^{2}$ .

Hence, the given statement is false as the area becomes

$4$ times when the side is doubled.

State whether the following statements are true (T) or false (F):
If the length of a rectangle is twice its breadth, then its area is constant.

0%
True
0%
False

Explanation

Let

$b$ be the breadth of the rectangle, then its length will be equal to

$2b$ .

Thus area of the rectangle is equal to

$(2b\times b)$ i.e.

$2b^2$

Hence area of the rectangle depends on the variable

$b$ .

Thus area of the rectangle is not constant. Hence given statement is false.

Side of a square garden in 30 m. If the scale used to draw its picture is 1cm: 5m, the perimeter of the square in the picture is

0%
20 cm
0%
24 cm
0%
28 cm
0%
30 cm

Explanation

The correct answer is option

$(b)$ .

Given, the side of a square garden =

$30\ m$

We know that, the perimeter of a square

$= 4\times \text{ side}$

So, the perimeter of a square garden

$= 4 \times 30 = 120\ m$

The scale used to draw its picture is

$1\ cm: 5\ m$

So, the perimeter of a square in the picture

$= 120 \div 5=24\ cm$

36 unit squares are joined to form a rectangle with the least perimeter. Perimeter of the rectangle is.

0%
12 units
0%
26 units
0%
24 units
0%
36 units

Explanation

Option (b) is correct.
Area of rectangle is 36 units
We have,

$\Rightarrow 36 = 6 \times 6$

$= 2\times 3 \times 3\times 2$

$=4\times 9$
Hence, the sides of a rectangle are

$4 \,cm$ and

$9\, cm$
Perimeter

$= 2(l+b)$

$=2(4+9)$

$=13\times 2$

$= 26\, units$

$12 \text{ m}^2$ is the area of.

0%
A square with side $12 \text{ m}$
0%
$12$ squares with side $1 \text{ m}$ each
0%
$3$ squares with side $4 \text{ m}$ each
0%
$4$ squares with side $3 \text{ m}$ each

Explanation

According to the option

$B,$

$12$ squares with side

$1\text{ m}$ each,
Area of

$1$ square

$= side \times side$
Area of

$12$ squares

$\Rightarrow 12 \times 1 \times 1 =12\text{ m}^2$ .

Hence, option

$B$ is correct.

The sides length of the top of square table is

$x$ . The expression for perimeter is:

0%
$4+x$
0%
$2x$
0%
$4x$
0%
$8x$

Explanation

$\bullet$ side length of the top of the table is

$x$

$\bullet$ Perimeter of a square

$=side+side+side+side =4 \times side$

$\bullet$ Therefore, perimeter of the square

$=4x$

$\bullet$ So, the expression for perimeter is

$4x$ .

$\textbf{Hence, the correct option is (c)}$

The perimeter of the rectangle whose length is

$60 \,cm$ and a diagonal is

$61 \,cm$ is

0%
$120 \,cm$
0%
$122 \,cm$
0%
$71 \,cm$
0%
$142 \,cm$

A rectangular piece of dimensions

$3\,cm \times 2\, cm$ was cut from a rectangular sheet of paper of dimensions

$6\, cm \times 5\, cm$ (Fig). Area of remaining sheet of paper is

0%
$30 \, cm^2$
0%
$36 \, cm^2$
0%
$24 \, cm^2$
0%
$22 \, cm^2$

Explanation

Option (c) is correct.
Given, Area of bigger rectangle

$=(6 \times 5)cm =30 \, cm^2$
Area of smaller rectangle

$= (3 \times 2)cm = 6 \, cm^2$
Therefore, area of remaining sheet of paper

$=$ Area of bigger rectangle

$-$ Area of smaller rectangle

$=(30 -6)= 24 \, cm^2$

Write the correct answer from the given four options.
A square board has an area of 144 square units. How long is each side of the board?

0%
11 units
0%
12 units
0%
13 units
0%
14 units

Explanation

Let

$a$ be the length of the sides of the square.

Area of square board =

$a^2$

$=144$

$a=\sqrt{144} = 12$ units

Is it true to say that area of a square inscribed in a circle of diameter

$p \,cm$ is

$p^2 \,cm^2$ ? Why ?

0%
True
0%
False

Explanation

The diameter of the circle is

$p$ cm.
So, the diagonal of the square will be

$p$ cm.
Now,

$AB^2 + BC^2 = AC^2$

$\Rightarrow AB^2 + AB^2 = p^2$

$\Rightarrow 2AB^2 = p^2$

$\Rightarrow AB = \dfrac{p}{\sqrt 2}$
Now, Area of square

$= \dfrac{p}{\sqrt 2} \times \dfrac{p}{\sqrt 2} = \dfrac{p^2}{2} \,cm^2$
Hence, the given statement is false.
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CBSE Questions for Class 6 Maths Mensuration Quiz 3 - MCQExams.com

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Practice Class 6 Maths Quiz Questions and Answers

CBSE Questions for Class 6 Maths Mensuration Quiz 3 - MCQExams.com

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Practice Class 6 Maths Quiz Questions and Answers

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