Mensuration Test

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Mensuration Test - 30

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Weekly Quiz Competition

Question 1
1 / -0

The addition of curved surface and circular surfaces are called

A
area

B
perimeter

C
lateral surface area

D
total surface area

Solution

The total surface area includes curved surface area and two circular surfaces.
Question 2
1 / -0

Find the area of the trapezoid.

A
100

B
200

C
300

D
400

Solution

Area of trapezoid $$=$$ $$\dfrac{h(a+b)}{2}$$
$$=$$ $$\dfrac{12(20+30)}{2}$$
$$= 300$$ $$unit^2$$
Question 3
1 / -0

The area of the given diagram is

A
$$14$$ sq. yards

B
$$49$$ sq. yards

C
$$25$$ sq. yards

D
$$21$$ sq. yards

Solution

Given, $$UT=6$$ yd, $$RS=8$$ yd, height $$=7$$ yards
Area of trapezoid $$=$$ $$\dfrac{1}{2}\times (l_{1}+l_{2})\times \text{height}$$
$$=$$ $$\dfrac{1}{2}\times (6+8)\times 7$$
$$=$$ $$\dfrac{1}{2}\times 14\times 7$$
$$= 49$$ sq. yards
Question 4
1 / -0

Find the surface area of a cube in square inches, whose each edge measures $$3$$ inches.

A
9

B
18

C
27

D
36

E
54

Solution

Surface area of cube$$=6a^2$$
Where '$$a$$' is the edge of the cube
Surface area $$=$$ $$6\times (3)^2$$
$$\Rightarrow 6\times 9=54$$ square inches
Question 5
1 / -0

What is the surface area of a cylinder that has a top and bottom if the height is $$8.5$$ units and the diameter is $$3$$ units?

A
$$18\pi$$ square units

B
$$30\pi$$ square units

C
$$32\pi$$ square units

D
$$36\pi$$ square units

E
$$54\pi$$ square units

Solution

Given: height $$= 8.5$$, diameter $$= 3$$
$$\therefore$$ radius $$=$$ $$\dfrac{D}{2}=\dfrac{3}{2}=1.5$$
Surface area $$=$$ $$2\pi rh +2\pi r^2$$
$$=2\pi\times1.5\times 8.5+2\pi\times 1.5^2$$
$$=2\pi(12.75+2.25)$$
$$=2\pi(15)$$
$$=30\pi$$ sq.units
Question 6
1 / -0

Figure $$ABCD$$ is a trapezoid with area $$50$$ square units. If the length of $$\overline{AB}$$ is $$6$$ units and the length of $$\overline {BC}$$ is $$5$$ units, what is the length of $$\overline {CD}$$?

A
$$4$$

B
$$5$$

C
$$6$$

D
$$10$$

E
$$14$$

Solution

Area of trapezoid $$=\dfrac { 1 }{ 2 } \left( AB+CD \right) \times BC=50$$ sq.units
$$\Rightarrow \quad \dfrac { 1 }{ 2 } \left( 6+CD \right) \times 5=50\Rightarrow 6+CD=\dfrac { 50\times 2 }{ 5 } \Rightarrow CD=20-6=14$$ units.
Question 7
1 / -0

A closed metallic cylindrical box is 1.25 m high and its base radius is 35 cm. If the sheet metal costs Rs. 80 per m$$^2$$, the cost of the material used in the box is

A
Rs. 281.60

B
Rs. 290

C
Rs. 340.50

D
Rs. 500

Solution

T.S.A. of cyl $$ = 2\pi rh+2\pi r^{2} = 2\pi \times \left ( \dfrac{35}{100} \right )\times 1.25+2\pi \left ( \dfrac{35}{100} \right )^{2} $$
$$ \Rightarrow TSA = 3.52\,m^{2} $$ & as cost of $$ 1\,m^{2} $$ is Rs 80
$$ \Rightarrow $$ Total cost $$ = 3.52\times 80 = Rs\,281.6 $$
Question 8
1 / -0

A room measures 11 ft x 12 ft x 9 ft. What is the volume?

A
1188 $$ft^3$$

B
32 $$ft^3$$

C
120 $$ft^3$$

D
1300 $$ft^3$$

E
1350 $$ft^3$$

Solution
Question 9
1 / -0

The curved surface area of a right circular cone of radius $$11.3$$ cm is $$355$$ cm$$^2$$. What is its slant height?

A
$$8$$ cm

B
$$9$$ cm

C
$$10$$ cm

D
$$11$$ cm

Solution

Given, radius $$r=11.3 \text{ cm}$$

and curved surface area $$=355 \text{ cm}^2$$.

We know, curved surface area of a cone $$ =\pi rl $$

$$11.3 \pi l= 355$$

$$l = \dfrac{355}{\pi \times 11.3}$$

$$ {l = 10\text{ cm}} $$

Therefore, option $$C$$ is correct.
Question 10
1 / -0

Each edge in a cube is $$5\ cm$$. What is the surface area in square cm?

A
$$25$$

B
$$30$$

C
$$100$$

D
$$125$$

E
$$150$$

Solution

Surface area of a cube is $$6a^2$$ where $$a$$ is an edge of the cube.

The surface area of the cube with edge $$5$$cm is given by:

$$A=6a^{ 2 }=6\times (5)^{ 2 }=6\times 25=150cm^{ 2 }$$

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Re-Attempt Weekly Quiz Competition

Mensuration Test - 30

Result

Mensuration Test - 30

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SHARING IS CARING

Question 1

area

perimeter

lateral surface area

total surface area

Solution

Question 2

100

200

300

400

Solution

Question 3

$$14$$ sq. yards

$$49$$ sq. yards

$$25$$ sq. yards

$$21$$ sq. yards

Solution

Question 4

9

18

27

36

54

Solution

Question 5

$$18\pi$$ square units

$$30\pi$$ square units

$$32\pi$$ square units

$$36\pi$$ square units

$$54\pi$$ square units

Solution

Question 6

$$4$$

$$5$$

$$6$$

$$10$$

$$14$$

Solution

Question 7

Rs. 281.60

Rs. 290

Rs. 340.50

Rs. 500

Solution

Question 8

1188 $$ft^3$$

32 $$ft^3$$

120 $$ft^3$$

1300 $$ft^3$$

1350 $$ft^3$$

Solution

Question 9

$$8$$ cm

$$9$$ cm

$$10$$ cm

$$11$$ cm

Solution

Question 10

$$25$$

$$30$$

$$100$$

$$125$$

$$150$$

Solution

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