Mensuration Test

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Mensuration Test - 34

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Weekly Quiz Competition

Question 1
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The diameter of the base of a right circular cylinder is $$21\mathrm { cm }$$ and its height is $$10\ \mathrm { cm }$$ . What is the area of the curved surface?

A
$$660\mathrm { cm } ^ { 2 }$$

B
$$930\mathrm { cm } ^ { 2 }$$

C
$$1320\mathrm { cm } ^ { 2 }$$

D
$$640\mathrm { cm } ^ { 2 }$$

Solution

$$Diameter =21\ cm$$
$$Radius=\dfrac{21}{2}\ cm$$
$$Height=10\ cm$$
We know that the curved surface area of the cylinder
$$=2\pi r h$$
$$=2\times \dfrac{22}{7}\times \dfrac{21}{2}\times 10$$
$$=220\times 3$$
$$=660\ cm^2$$
Question 2
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The diameter of a cylinder is $$28$$cm and its height is $$20$$cm find the curved surface area.

A
$$1760$$sq.cm

B
$$17600$$sq.cm

C
$$1706$$sq.cm

D
none of these

Solution

Diameter of the cylinder $$=28$$cm

$$\therefore$$ Radius of the cylinder $$=\dfrac{28}{2}$$
$$=14$$cm

Height of the cylinder $$=20$$cm

$$\text{Curved surface area}=2\pi rh\\=2\times \dfrac{22}{7}\times 14\times 20\\=1760\ sq.cm$$
Question 3
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The diameter of a cylinder is $$28$$cm and its height is $$20$$cm find the total surface area.

A
$$2992$$

B
$$2090$$

C
$$2900$$

D
$$2099$$

Solution

Diameter of the cylinder$$=28$$cm

$$\therefore$$ Radius of the cylinder$$=r=\dfrac{28}{2}=14$$cm

Height of the cylinder$$=h=20$$cm

Total surface area $$=2\pi r\left(r+h\right)$$

$$=2\times\dfrac{22}{7}\times 14\times\left(14+20\right)$$

$$=2992$$sq.cm
Question 4
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The area of trapezium $$ABCD$$ is

A
$$24 sq.cm$$

B
$$28 sq.cm$$

C
$$26 sq.cm$$

D
$$22sq.cm$$

Solution

Area of a trapezium$$=\dfrac{1}{2}\times$$(Sum of parallel sides)$$\times$$distance between them.
$$=\dfrac{1}{2}\times\left(6+8\right)\times 4$$
$$=14\times 2\\=28\ sq.cm$$
$$\therefore$$Area of a trapezium$$=28$$sq.cms
Question 5
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The area of given trapezium is

A
$$\dfrac{1}{2}d_{1}\times d_{2}\dfrac{1}{2}d_{1}\times d_{2}$$

B
$$a\times b$$

C
$$\dfrac{1}{2}\left(a+b\right)h$$

D
$$none\ of\ these$$

Solution
Question 6
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Volume of a rectangular box (cuboid) with length $$=2ab,$$ breadth $$=3ac$$ and height $$=2ac$$ is

A
$$12a^2bc^2$$

B
$$12a^3bc^2$$

C
$$12a^2bc$$

D
$$2ab+3ac+2ac$$

Solution

Given

Length $$=2ab$$

Breadth $$=3ac$$

Height $$=2ac$$

Volume of cuboid $$=$$ length $$\times$$ breadth $$\times$$ height

$$=2ab\times 3ac\times 2ac$$

$$=12a^3bc^2$$

$$\therefore$$ Hence the correct answer is $$12a^3bc^2$$.
Question 7
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Find the total surface area of the cuboids of length, breadth and height
$$12 \mathrm { cm } , 10 \mathrm { cm } , 5 \mathrm { cm }$$ respectively.

A
$$460 \ cm^2$$

B
$$490 \ cm^2$$

C
$$360 \ cm^2$$

D
$$230 \ cm^2$$

Solution
Question 8
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Mark the correct alternative of the following.
The number of surfaces of a hollow cylindrical object is?

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution

The hollow cylinder has a total of 4 surfaces, inner and outer curved surfaces and the ring lies at the base of the cylinder and the top of the cylinder
Question 9
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Mark the correct alternative of the following.
A cylinder with radius $$r$$ and height $$h$$ is closed on the top and bottom. Which of the following expressions represents the total surface area of this cylinder?

A
$$2\pi r(r+h)$$

B
$$\pi r(r+2h)$$

C
$$\pi r(2r+h)$$

D
$$2\pi r^2+h$$

Solution

Let $$S$$ be the total surface area of the closed cylinder with radius $$r$$ and height $$h$$, then,
Total surface area of this cylinder $$(S)= 2πrh + πr^2+ πr^2$$
$$\Rightarrow$$ $$S=2\pi r^2+2\pi r h$$
$$\Rightarrow$$ $$S=2\pi r(r+h)$$
Question 10
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A right circular cylindrical tunnel of diameter $$2$$m and length $$40$$m is to be constructed from a sheet of iron. The area of the iron sheet required in $$m^2$$, is?

A
$$40\pi$$

B
$$80\pi$$

C
$$160\pi$$

D
$$200\pi$$

Solution

Let $$r$$ be the radius of the cylinder and $$h$$be its height.
It is given that,
$$d=2\,m$$
Then, $$r=\dfrac{2m}{2}=1\,m$$
$$h=40\,m$$
$$\therefore$$ Total surface area of sheet required is:
$$\Rightarrow$$ $$S=2\pi rh$$
$$=2\pi\times 1\times 40$$
$$=80\pi \,m^2$$