Mensuration Test

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Mensuration Test - 28

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Weekly Quiz Competition

Question 1
1 / -0

Calculate the area of a trapezium whose parallel sides are $$22$$ and $$10$$ m, and a height of $$15$$ m.

A
$$240$$ $$m^{2}$$

B
$$230$$ $$m^{2}$$

C
$$220$$ $$m^{2}$$

D
$$210$$ $$m^{2}$$

Solution

Area of a trapezoid = $$\dfrac{b_{1}+ b_{2}}{2}\times h$$
= $$\dfrac{12 + 10}{2}\times 15$$
= $$\dfrac{32}{2}\times 15$$
= $$240$$ $$m^{2}$$
Question 2
1 / -0

A company packages its juice in a tetra pack shown below. How much quantity of juice does it contain.

A
$$\displaystyle 140{ cm }^{ 3 }$$

B
$$\displaystyle 160{ cm }^{ 3 }$$

C
$$\displaystyle 16{ cm }^{ 3 }$$

D
$$\displaystyle 136cm^3$$

Solution

Quantity of juice in the package $$=$$ Volume of cuboidal package
$$ =$$ $$l\times b\times h$$
$$=$$ $$4\times 4\times 10$$
$$=$$ $$160$$ $${ cm }^{ 3 }$$
Question 3
1 / -0

Edward bought a container of ceralac in the shape of cylinder. If the container has a radius $$10 m$$ and a surface area is $$\displaystyle 340\pi $$. What is its height?

A
$$5 m$$

B
$$6m$$

C
$$7m$$

D
$$8m$$

Solution

Surface area of cylinder is $$A=2πr(r+h)$$

Here the cylindrical container has surface area $$A=340π$$ m$$^2$$ and radius $$r=10$$ m.

Thus,

$$A=2πr(r+h)\\ \Rightarrow 340π=2π\times 10(10+h)\\ \Rightarrow 340π=20π(10+h)\\ \Rightarrow 340π=200π+20πh\\ \Rightarrow 20πh=340π-200π\\ \Rightarrow 20πh=140π\\ \Rightarrow h=\dfrac { 140π }{ 20π } =7$$

Hence, the height of the cylindrical container is $$7m$$.
Question 4
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The area of the trapezium is $$100\ { m }^{ 2 }$$ and height is $$10\ m.$$ Find the length of one parallel side if the length of the other parallel side is $$5\ m.$$

A
$$5\ m$$

B
$$10\ m$$

C
$$15\ m$$

D
$$20\ m$$

Solution

Consider that $$A$$ is the area of the trapezium, $$a, b$$ are the length of the parallel sides, and $$h$$ is the height of the trapezium.

Given:
$$A=100\ m^2$$
$$h=10\ m$$
$$a=5\ m$$

So,
$$\begin{aligned}{}A &= \frac{1}{2} \times \left( {a + b} \right) \times h\\100 &= \frac{1}{2} \times \left( {5 + b} \right) \times 10\\20 &= 5 + b\\b &= 15\ m\end{aligned}$$

Hence, option $$C$$ is correct.
Question 5
1 / -0

Fill in the blank:
____________ is the measure of the amount of space inside of a solid figure, like a cube, ball, cylinder or pyramid.

A
Mass

B
Volume

C
Capacity

D
Density

Solution

Volume is the measure of the amount of space inside of a solid figure, like a cube, ball, cylinder or pyramid.
Question 6
1 / -0

A swimming pool is 100 m long and 15 m wide its deep and 24 m height respectively. Find the capacity of the pool.

A
36,000 m

B
36,000 $$m^3$$

C
36,000 $$m^2$$

D
36,000 $$cm$$

Solution

Volume of the pool = $$l \times b \times h$$
= $$100 \times 15 \times 24$$
= $$36000 m^3$$
Question 7
1 / -0

A brick whose length, breadth and height are $$5m, 6m$$, and $$7m$$ respectively. Find the surface area of the brick.

A
$$214\ m^2$$

B
$$202\ m^2$$

C
$$201\ m^2$$

D
$$210\ m^2$$

Solution

Surface area of the cuboid having length, breadth and height as $$l, b$$ and $$h$$ respectively is given as $$2 (lb + bh + hl)$$

Brick has the shape of cuboid. Let $$S$$ be the require surface area.

$$S=2 (5 \times 6 + 6 \times 7 + 7 \times 5)$$

$$2 (30 + 42 + 35)$$

$$214 m^2$$
Question 8
1 / -0

Fill in the blank: The volume of solid objects is measured in _____ units.

A
Cubic

B
Square

C
Meter

D
Liter

Solution

The volume of solid objects is measured in cubic units.
Question 9
1 / -0

Find the surface area of a cylinder with the following dimension:
Height $$= 10$$ ft.
Radius $$= 2$$ ft.

A
$$\displaystyle 82\pi { ft }^{ 2 }$$

B
$$\displaystyle 78\pi { ft }^{ 2 }$$

C
$$\displaystyle 48\pi { ft }^{ 2 }$$

D
$$\displaystyle 81\pi { ft }^{ 2 }$$

Solution

Surface area of cylinder is $$A=2πr(r+h)$$

Here, radius is $$r=2$$ ft and the height is $$h=10$$ ft.

Thus,

$$A=2π\times 2(2+10)=2π\times 2\times 12=48π$$

Hence, the surface area of the cylinder is $$48π$$ ft$$^2$$.
Question 10
1 / -0

If lateral surface area of a cylinder of height 10 cm is 100 cm $$^{ 2 }$$, find radius of its base.

A
$$\displaystyle 5\pi $$

B
$$\displaystyle \frac {5}{\pi}$$

C
$$\displaystyle 6\pi $$

D
$$\displaystyle \frac { \pi }{ 5 } $$

Solution

Given that, the lateral surface area of a cylinder of height $$10\ cm$$ is $$100\ cm^2$$.
To find out: The radius of the base of the cylinder.

We know that, lateral surface area of a cylinder is $$\displaystyle 2\pi rh$$
$$\therefore \ 2\pi rh=100\\$$
$$\Rightarrow 2\pi r (10)=100\\$$
$$\Rightarrow 20\pi r =100\\$$
$$\Rightarrow r =\dfrac{100}{20\pi}\\$$
$$\therefore \ \displaystyle r=\dfrac { 5 }{ \pi }$$

Hence, the radius of the base of the given cylinder is $$\dfrac { 5 }{ \pi }$$.

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Re-Attempt Weekly Quiz Competition

Mensuration Test - 28

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Mensuration Test - 28

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Question 1

$$240$$ $$m^{2}$$

$$230$$ $$m^{2}$$

$$220$$ $$m^{2}$$

$$210$$ $$m^{2}$$

Solution

Question 2

$$\displaystyle 140{ cm }^{ 3 }$$

$$\displaystyle 160{ cm }^{ 3 }$$

$$\displaystyle 16{ cm }^{ 3 }$$

$$\displaystyle 136cm^3$$

Solution

Question 3

$$5 m$$

$$6m$$

$$7m$$

$$8m$$

Solution

Question 4

$$5\ m$$

$$10\ m$$

$$15\ m$$

$$20\ m$$

Solution

Question 5

Mass

Volume

Capacity

Density

Solution

Question 6

36,000 m

36,000 $$m^3$$

36,000 $$m^2$$

36,000 $$cm$$

Solution

Question 7

$$214\ m^2$$

$$202\ m^2$$

$$201\ m^2$$

$$210\ m^2$$

Solution

Question 8

Cubic

Square

Meter

Liter

Solution

Question 9

$$\displaystyle 82\pi { ft }^{ 2 }$$

$$\displaystyle 78\pi { ft }^{ 2 }$$

$$\displaystyle 48\pi { ft }^{ 2 }$$

$$\displaystyle 81\pi { ft }^{ 2 }$$

Solution

Question 10

$$\displaystyle 5\pi $$

$$\displaystyle \frac {5}{\pi}$$

$$\displaystyle 6\pi $$

$$\displaystyle \frac { \pi }{ 5 } $$

Solution

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