Mensuration Test

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Mensuration Test - 16

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Weekly Quiz Competition

Question 1
1 / -0

The formula to find the total surface area of a Rs.$$5$$ coin is ..............

A
$$\pi { r }^{ 2 }h$$

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

C
$$\pi { r }^{ 3 }h$$

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

Solution

A $$5$$ rupee coin is cylindrical in shape having radius $$r$$ and haight $$h$$.
TSA of a cylinder is given by $$2\pi r(r+h)$$
Thus, the total surface area of the cylinder can be calculated by using the formula $$2\pi r(h+r)$$
Hence, option D is correct.
Question 2
1 / -0

If all three parameters of a cuboid are in meters$$(m)$$, then unit of volume of a cuboid is:

A
$$m$$

B
$$m^{2}$$

C
$$m^{3}$$

D
$$cm^{3}$$

Solution

As the volume of a cube is $$length\times length \times length $$
If lengths of all are measured in meters.
Then the volume will be measured in $$m^3$$.
Hence, the answer is $$m^{3}$$.
Question 3
1 / -0

The surface area of a cube of side $$27\ \text{cm}$$ is

A
$$2916\ \text{cm}^{2}$$

B
$$729\ \text{cm}^{2}$$

C
$$4374\ \text{cm}^{2}$$

D
$$19683\ \text{cm}^{2}$$

Solution

Let, the given side of square$$=a=27\ \text{cm}$$
Surface area of cube$$=6a^2$$
$$=6(27)^2\ \text{cm}^2$$
$$=4374\ \text{cm}^2$$
Question 4
1 / -0

Find the surface area of a $$10cm \times 4cm \times 3cm$$ brick:

A
84 sq. cm

B
124 sq.cm

C
164 sq.cm

D
180 sq.cm

Solution

The formula for calculating the surface area of a cuboid of dimensions :

$$ l \times b \times h $$ is :

$$ 2\times (l\times b+b\times h+h\times l) $$

Substituting,

$$l=10cm$$

$$b=4cm$$

$$h=3cm$$

Surface area = $$ 2\times (10\times 4+4\times 3+3\times 10) $$

$$ = 2\times (40 + 12 + 30) $$

$$ = 2\times 82 { cm }^{ 2 } $$

$$ = 164 { cm }^{ 2 } $$

Hence, the answer is option (C)
Question 5
1 / -0

If the height of a cylinder becomes 1/4 of the original height and the radius is doubled, then which of the following will be true

A
Curved surface area of the cylinder will be doubled.

B
curved surface area of the cylinder will remain unchanged.

C
Curved surface area of the cylinder will be halved.

D
Curved surface area will be 1 4 of the original curved surface.

Solution

(c) Curved surface area of the cylinder will be halved.
Let the new height and radius be h / 4 and 2 r respecitvely,
where r and h are original radius and original height of the cylinder respectively.
We know that, curved surface are of cylinder= $$ 2\pi r h $$
Then, curved surface of the new cylinder =
= 2\pi (2r) $$ \times \dfrac{1}{4}h=4 \pi r\times \dfrac{1}{4}h= 2 \pi rh $$
= $$ \dfrac{1}{2}\times 2\pi rh $$ [multiplying and dviding by 2 ]
= $$ \dfrac{1}{2} $$ original curved surface area.
Question 6
1 / -0

If the height of a cylinder becomes 1/4 of the original height and the radius is doubled, then which of the following will be true

A
Total surface area of the cylinder will be doubled.

B
Total surface area of the cylinder will remain unchanged.

C
Total surface of the cylinder will be halved.

D
None of the above.

Solution

(d) None of the above.
We know that,
Total surface area of cylinder having radius r and height h= $$ 2\pi r(h+r) $$
Total surface area of the cylinder with new height $$ \left ( \dfrac{h}{u} \right ) $$ and
radius 2r = $$ 2\pi (2r)\left ( 2r+\frac{1}{4}h \right ) $$
= 4 $$ \pi r(8r+h)\times \dfrac{1}{4} $$
= $$ \pi r(8 r+h) $$
Question 7
1 / -0

If the radius of a cylinder is tripled but its curved surface area is unchanged, then its height will be

A
Tripled

B
Constant

C
One sixth

D
One third

Solution

(d) One third
Let us take h' as new height
Curved surface area of a cylinder with radius r and height h= $$ 2\pi r h $$
New Radius = 3r
Curved surface area = $$ 2\pi \times 3r \times h $$ = $$ 2 \pi rh $$
$$ \Rightarrow $$ $$ 6 \pi r \times h $$ = $$ 2\pi rh $$
$$ \Rightarrow $$ h' = $$ 2\pi rh $$/ $$ 6\pi rh $$
Therefore, h' = $$ \dfrac{1}{3}h $$
Question 8
1 / -0

The area of a trapezium is $$34\;{ cm }^{ 2 }$$ and the length of one of the parallel sides is $$10\; cm$$ and its height is $$4\; cm$$. Find the length of the other parallel side in $$cm$$.

A
$$4$$

B
$$21$$

C
$$7$$

D
$$14$$

Solution

Area of trapezium $$=\cfrac { 1 }{ 2 } ({ b }_{ 1 }+{ b }_{ 2 })\times h=34\: cm^2$$
Where $${ b }_{ 1 }=$$ One parallel side of trapezium $$=10\: cm$$
$${ b }_{ 2 }=$$ Other parallel side of trapezium $$=b\: cm$$
$$h =$$ height of trapezium $$=4\: cm$$

Area of trapezium$$=34cm^2$$

$$\Rightarrow 34=\dfrac{10+b}{2} \times 4$$

$$\Rightarrow b+10=17 $$

$$\Rightarrow b = 7\: cm$$
Question 9
1 / -0

The area of a filed in the shape of a trapezium measures 1440 m. The perpendicular distance between its parallel sided is 24 m. If the ratio of the parallel sides is 5:3, the length of the longer parallel side is

A
$$45 m$$

B
$$60 m$$

C
$$75 m$$

D
$$120 m$$

Solution

Area of trapezium $$=\dfrac{1}{2}$$ (sum of parallel sides) $$\times $$ height
$$=\dfrac{1}{2}(5x+3x)\times 24=1440.$$
Solving, we get $$x=15$$ and length of longer side $$=5\times 15=75m.$$
Question 10
1 / -0

The shape of the top surface of a table is a trapezium. Find its area in $$cm^2$$ if its parallel sides are $$1$$ m and $$1.2$$ m and perpendicular distance between them is $$0.8$$ m.

A
$$880\: cm^2$$

B
$$88\: cm^2$$

C
$$8800\:cm^2$$

D
$$8.8\:cm^2$$

Solution

Length of parallel sides is given as $$1\:m = 100$$ cm and $$1.2$$ m $$= 120 $$ cm
Height $$(h) = 0.8$$ m $$= 80$$ cm
Area of trapezium $$=\left[\dfrac{100+120}{2}\right] (80)= 8800\: cm^2$$

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Mensuration Test - 16

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Mensuration Test - 16

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Question 1

$$\pi { r }^{ 2 }h$$

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

$$\pi { r }^{ 3 }h$$

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

Solution

Question 2

$$m$$

$$m^{2}$$

$$m^{3}$$

$$cm^{3}$$

Solution

Question 3

$$2916\ \text{cm}^{2}$$

$$729\ \text{cm}^{2}$$

$$4374\ \text{cm}^{2}$$

$$19683\ \text{cm}^{2}$$

Solution

Question 4

84 sq. cm

124 sq.cm

164 sq.cm

180 sq.cm

Solution

Question 5

Curved surface area of the cylinder will be doubled.

curved surface area of the cylinder will remain unchanged.

Curved surface area of the cylinder will be halved.

Curved surface area will be 1 4 of the original curved surface.

Solution

Question 6

Total surface area of the cylinder will be doubled.

Total surface area of the cylinder will remain unchanged.

Total surface of the cylinder will be halved.

None of the above.

Solution

Question 7

Tripled

Constant

One sixth

One third

Solution

Question 8

$$4$$

$$21$$

$$7$$

$$14$$

Solution

Question 9

$$45 m$$

$$60 m$$

$$75 m$$

$$120 m$$

Solution

Question 10

$$880\: cm^2$$

$$88\: cm^2$$

$$8800\:cm^2$$

$$8.8\:cm^2$$

Solution

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