Mensuration Test

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Mensuration Test - 23

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Weekly Quiz Competition

Question 1
1 / -0

If the area of the trapezium is 312 $$\displaystyle cm^{2}$$ then the distance between the parallel sides whose lengths are 21 cm and 27 cm respectively is:

A
13 cm

B
14 cm

C
15 cm

D
16 cm

Solution

Given: The area of trapezium is $$312cm^2$$ and the length of two parallel sides are $$21 cm$$ and $$27 cm$$.

We know that the area of trapezium $$=\dfrac{1}{2}\times (\text {sum of parallel sides})(\text {Distance between parallel sides})$$

$$=\dfrac{1}{2}(21+27)x$$ (where $$x$$ is the distance between parallel sides)

But given the area $$= 312cm^2$$

$$\therefore \dfrac{1}{2}(27+21)x=312$$

$$\Rightarrow 24x=312$$

$$\Rightarrow x=13$$ cm

Therefore, the distance between parallel sides $$=13 cm$$.
Question 2
1 / -0

The volume of a cube whose edge measures 12 m is ............ times the volume of a cuboid of dimensions 8 m $$\times$$ 6 m $$\times $$ 4 m

A
6

B
7

C
5

D
9

Solution

Volume of the cube $$= 12 \times 12 \times 12 = 1,728 $$ cu m
Volume of the cuboid $$= 8 \times 6 \times 4 = 192 $$ cu m
$$\displaystyle \frac{1728}{192} = 9 times$$
Question 3
1 / -0

What is the volume of the cuboid of the brick? (Given : length $$= 23$$ cm, breadth $$= 10$$ cm, height $$= 12$$ cm)

A
$$\displaystyle 2765{ cm }^{ 3 }$$

B
$$\displaystyle 2760{ cm }^{ 3 }$$

C
$$\displaystyle 2340{ cm }^{ 3 }$$

D
$$\displaystyle 2901{ cm }^{ 3 }$$

Solution

$$Volume\ of\ cuboid=length\times breadth\times height$$
$$length=223\ cm$$
$$breadth=10\ cm$$
$$height=12\ cm$$
$$volume=23\times 10\times 12=2760\ cm^3$$
Question 4
1 / -0

Find the volume of this rectangular prism (cuboid). $$($$Given: $$L = 2$$ cm, $$B = 10$$ cm, $$H = 30$$ cm$$)$$

A
$$\displaystyle 600\ { cm }^{ 3 }$$

B
$$\displaystyle 760\ { cm }^{ 3 }$$

C
$$\displaystyle 42\ { cm }^{ 3 }$$

D
$$\displaystyle 500\ { cm }^{ 3 }$$

Solution

Volume of the cuboid $$=$$ length $$\times$$ breadth $$\times$$ height
Therefore, length $$= 2$$ cm, breadth $$= 10$$ cm, height $$= 30$$ cm
Volume of the cuboid $$=$$ $$\displaystyle 2\times 10\times 30=600{ cm }^{ 3 }$$
Question 5
1 / -0

One of the parallel sides of a trapezium is double of the other. The perpendicular distance between the two parallel sides is 12 cm. If the area of the trapezium is 180 $$cm^2$$, find the length of the sides of the trapezium.

A
10 cm, 30 cm

B
10 cm, 20 cm

C
20 cm, 40 cm

D
5 cm, 10 cm

Solution

Let the lengths of the two parallel sides of the trapezium be $$x$$ cm and $$2x$$ cm respectively.
We know that
Area of the trapezium
= $$\displaystyle \frac{1}{2}$$ (Sum of parallel sides) $$\times$$ (Distance between them)
$$\therefore 180 = \displaystyle \frac{1}{2} (x + 2x) \times 12$$
or $$180 \times 2 = 3x \times 12$$
or $$180 \times 2 = 3x \times 12$$
or $$ 36x = 360$$
or $$x =10$$
$$\therefore$$ The sides of the trapezium are 10 cm and 20 cm respectively.
Question 6
1 / -0

If the side of cube is $$2\text{ m}$$, then surface area of cube is

A
$$24\:\text{m}^2$$

B
$$124\:\text{m}^2$$

C
$$24\:\text{m}$$

D
$$124\:\text{m}$$

Solution

Given, side of a cube $$=2\text{ m}$$
Let $$'a'$$ be the length of the side of the cube.
Surface area of the cube $$=$$ $$6 \times a^2$$
$$= 6 \times 2^2$$
$$=6 \times 4$$
$$=24 \text{ m}^2$$
So, option A is correct.
Question 7
1 / -0

A square sheet of side $$28$$ cm is folded into a cylinder by joining its two sides. Find the base area of the cylinder thus formed (in $$\displaystyle cm^{2}$$).

A
$$\displaystyle \frac{524}{11}$$

B
$$\displaystyle \frac{575}{11}$$

C
$$\displaystyle \frac{629}{11}$$

D
$$\displaystyle \frac{686}{11}$$

Solution

As the square sheet is folded to form a cylinder, circumference of the base of the cylinder will be equal to $$ 28 $$ cm
Let $$R$$ be the radius of the cylinder
Circumference of base of cylinder $$ = 2 \pi R $$
So, $$ 2 \times \dfrac {22}{7} \times R = 28 $$
$$ \Rightarrow R = \dfrac {49}{11} $$
And area of the base of the cylinder $$ = \pi{R}^{2} $$
$$= \dfrac {22}{7} \times \dfrac {49}{11} \times \dfrac {49}{11} $$
$$ = \dfrac {686}{11} $$ sq.cm
Question 8
1 / -0

A cuboidal container has dimensions of $$20$$ cm $$\times$$ $$18$$ cm $$\times$$ $$16$$ cm. Find the maximum number of syrup bottles whose contents can be emptied into the container, if each bottle contains $$24$$ $$\displaystyle cm^{3}$$ of syrup.

A
$$120$$

B
$$180$$

C
$$240$$

D
$$270$$

Solution

As the container is cuboidal, its volume $$=$$ length $$\times$$ breadth $$\times $$ height

So, amount of syrup contained in it $$ = (20 \times 18 \times 16)\ cm^3 $$

Given: Each syrup bottle can contain $$ 24\ {cm}^{3} $$ of syrup

The number of bottles that can be filled $$ = \dfrac {20 \times 18 \times 16 }{24} = 240 $$
Question 9
1 / -0

Capacity is not measured in ..........

A
Litres

B
Millilitres

C
Cubic centimetres

D
Centimetres

Solution
Question 10
1 / -0

The side of a cube 4 cm. Its area is---

A
16 sq. cm

B
64 sq. cm

C
12 sq. cm

D
None of these

Solution

TSA of a cube $$= 4$$ $$\times \,\, (Side)^2$$
$$= 4$$ $$\times \,\, (4)^2$$ sq. cm
$$= 4$$ $$\times$$ 16 sq. cm
$$= 64$$ sq. cm

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Mensuration Test - 23

Result

Mensuration Test - 23

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Question 1

13 cm

14 cm

15 cm

16 cm

Solution

Question 2

6

7

5

9

Solution

Question 3

$$\displaystyle 2765{ cm }^{ 3 }$$

$$\displaystyle 2760{ cm }^{ 3 }$$

$$\displaystyle 2340{ cm }^{ 3 }$$

$$\displaystyle 2901{ cm }^{ 3 }$$

Solution

Question 4

$$\displaystyle 600\ { cm }^{ 3 }$$

$$\displaystyle 760\ { cm }^{ 3 }$$

$$\displaystyle 42\ { cm }^{ 3 }$$

$$\displaystyle 500\ { cm }^{ 3 }$$

Solution

Question 5

10 cm, 30 cm

10 cm, 20 cm

20 cm, 40 cm

5 cm, 10 cm

Solution

Question 6

$$24\:\text{m}^2$$

$$124\:\text{m}^2$$

$$24\:\text{m}$$

$$124\:\text{m}$$

Solution

Question 7

$$\displaystyle \frac{524}{11}$$

$$\displaystyle \frac{575}{11}$$

$$\displaystyle \frac{629}{11}$$

$$\displaystyle \frac{686}{11}$$

Solution

Question 8

$$120$$

$$180$$

$$240$$

$$270$$

Solution

Question 9

Litres

Millilitres

Cubic centimetres

Centimetres

Solution

Question 10

16 sq. cm

64 sq. cm

12 sq. cm

None of these

Solution

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