Mensuration Test

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Mensuration Test - 7

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Weekly Quiz Competition

Question 1
1 / -0

The total surface area of a cube is 216 cm². What is its edge length?

A
6 cm

B
cm

C
cm

D
cm

Solution

If a is the edge length of a cube, then the total surface area of the cube is 6a².

= 216 cm²
The edge length of the cube (a) = = = 6 cm.
Question 2
1 / -0

Let 'a' and 'b' respectively be the radius of the base and the height of a right circular cylinder. Which of the following expressions represents the ratio of its curved surface area to its total surface area?

A

B

C

D

Solution

Radius of the base of the cylinder = a
Height of the cylinder = b
Question 3
1 / -0

The length, breadth, height, volume, total surface area, and lateral surface area of a cuboidal box are , b, h, v, S₁ and S₂, respectively. Which of the following relations is true?

A
=

B
b =

C
S₁ = 2h( + b)

D
S₂ = 2(b + bh + h)

Solution

Volume of a cuboid (V) = length breadth height
Thus, V = b h
Or b =
Question 4
1 / -0

The radii of two cylinders are in the ratio 4 : 3 and their heights are in the ratio 7 : 2. The ratio of their volumes is

A
16 : 9

B
49 : 3

C
14 : 3

D
56 : 9

Solution

Ratio of radii =

Ratio of heights =

Volume of a cylinder =

Ratio of volumes =
=
=
=
Question 5
1 / -0

Two cubes of edge 8 cm each are joined. What is the volume of the resultant solid?

A
256 cm³

B
512 cm³

C
1014 cm³

D
1024 cm³

Solution

Volume of each cube = (8 8 8) cm³
Volume of the resultant solid = 2 8 8 8 cm³ = 1024 cm³
Question 6
1 / -0

If V, p and q are the volume, base radius and height of a right circular cylinder, respectively, then which of the following relationships is true?

A
= 2p

B
Vp = q

C
= q

D
= q²

Solution

Volume of the cylinder = r²h …. (1)
Given, volume = V
Radius = p
Height = q
Substituting the values in (1), we get
V = p²q
Question 7
1 / -0

The perimeter of a rhombus is 240 m and the distance between any two parallel sides is 20 m. The area of the rhombus (in sq.m) is

A
600

B
1200

C
2400

D
4800

Solution

Perimeter of the rhombus = 240 m
Each side of the rhombus = 60 m
Since rhombus is also a parallelogram,
Area = base × height = 60 m × 20 m = 1200 m²
Hence, answer option 2 is correct.
Question 8
1 / -0

Calculate the volume (in cm³) of the given solid.

A
^{_{30 + 6}}

B
^{_{30 + 10}}

C
30 + 4

D
30 + 12

Solution

Volume of the given solid = Volume of cuboid + Volume of cylinder
= (l b h₁) + πr²h₂
= (5 cm 3 cm 2 cm) + π(2 cm)² (3 cm)
= (30 + 12π) cm³
Question 9
1 / -0

A right circular cylinder of height 15 cm and radius 7 cm is melted and recast into two identical cylinders, each of height 7.5 cm. What is the base radius of each cylinder?

A
7 cm

B
9.8 cm

C
7.5 cm

D
49 cm

Solution

If h₁ is the height and r₁ is the radius of the bigger cylinder and h₂ is the height and r₂ is radius of the small cylinder, then the volume of the cylinder = πr²h
Now, the volume of the bigger cylinder = 2 × (volume of each smaller cylinder)
π (7)² 15 = 2 ( (7.5))
=
= 49
r₂ = 7 cm
So, the radius of each smaller cylinder = 7 cm
Question 10
1 / -0

If the volume of a cuboid is 1000 m³ and the area of its base is 50 m², then what is the height of the cuboid?

A
21 m

B
20 m

C
60 m

D
70 m

Solution

Volume of cuboid = V
Area of base of cuboid = A
Height of the cuboid = h
A × h = V
h =
Question 11
1 / -0

A rectangular tank of length and breadth 2 m and 1.25 m respectively is half full. If 500 litres of water is poured into the tank, the rise of water-level in the tank will be

A
20 cm

B
30 cm

C
35 cm

D
40 cm

Solution

Let H be the rise in water-level when 500 litres of water is poured into the tank.

Then, according to the question,

200 × 125 × H = 500 × 1000 (Converted m to cm and litres to cc)

H = = 20 cm
Question 12
1 / -0

A cylindrical roller of diameter 140 cm covered an area of 220 sq. m in 20 revolutions. Find the length of the roller.

A
1.25 m

B
2.5 m

C
3 m

D
50 m

Solution

Suppose, length of the roller = h
Number of revolutions = 220

h = 2.5 m
Hence, length of the roller = 2.5 m
Question 13
1 / -0

Find the area swept by minute hand in 15 minutes if the length of the minute hand is 15 cm.

A
179.500 cm²

B
178.566 cm²

C
176.786 cm²

D
176.468 cm²

Solution

Given, radius of the minutes hand = 15 cm
In 15 minutes, the minute hand of a clock rotates by 90°.
∴ Area covered by minute hand in 15 minutes =
= 176.786 cm²
Hence, answer option 3 is correct.
Question 14
1 / -0

Find the breadth of a swimming pool whose length is 40 m and the ratio of numerical values of its area (in m²) and perimeter (in m) is 20 : 12. The pool is rectangular in shape.

A
20/11 m

B
30/11 m

C
40/11 m

D
25/11 m

Solution

480b = 1600 + 40b

480b - 40b = 1600

b = 1600/440 = 40/11

Where b is the breadth of the pool in metres.

Hence, answer option 3 is correct.
Question 15
1 / -0

A circular stage is to be made in a school. The radius of the stage is 30 m. Now a circular pavement of 10 m width is to be made around it. This has to be covered with red carpet. The cost of red carpet is Rs. 15 per square m. What will be the total cost of carpeting?

A
Rs. 35,000

B
Rs. 34,000

C
Rs. 33,600

D
Rs. 33,000

Solution

Area of the circular stage = π(30)² m² = 900π m²
Area including the circular stage and the circular path = 1600π m²
So, area of the circular path = π[(1600 - 900] m² = 700 πm² = 2200 m²
Cost of covering the path with red carpet = Rs. 2200 × 15 = Rs. 33,000
Hence, answer option 4 is correct.
Question 16
1 / -0

^{_{Nikhil`s father bought a cake of dimensions 12 cm}_{15 cm}_{10 cm. If he served each of his friends a piece of cake of dimensions 5 cm}_{2 cm}_{6 cm, then how many friends ate the cake?}}

A
10

B
20

C
30

D
40

Solution

Volume of the cake = (12 15 10) cm³
Volume served to each friend = (5 2 6) cm³ Number of friends who ate the cake

=

=

= 2 3 5 = 30
Question 17
1 / -0

A wooden box measures externally 4 m × 3 m × 2 m. The thickness of all four sides is 5 cm. If the capacity of the box is 18.096 m³, find the thickness of the bottom.

A
0.3 m

B
0.1 m

C
0.2 m

D
0.4 m

Solution

Let the thickness of the bottom = x m
Then, volume = 18.096 m³
(4 - 0.10) × (3 - 0.10) × (2 - 2x) = 18.096
2 - 2x = 1.6
x = 0.2
So, thickness of the bottom is 0.2 m.
Question 18
1 / -0

A field is in the form of a triangle with the base being three times its altitude. If the cost of cultivating the field at Rs. 24.68 per hectare is Rs. 333.18, then find the base and altitude of the triangle made.

A
B = 600 m, A = 200 m

B
B = 300 m, A = 100 m

C
B = 900 m, A = 300 m

D
None of these

Solution

Area of the field =
= 13.5 hectares
= 13.5 × 10,000 m²
Area of the field = × 3h × h
13.5 × 10,000 = h²
h = 300 m = Altitude
Altitude = A = 300 m
Base = B = 900 m
Answer: (3)
Question 19
1 / -0

A rectangular sheet with dimensions 22 m × 10 m is rolled into a cylinder such that the smaller side becomes the height of the cylinder. What is the volume of the cylinder so formed?

A
365 m³

B
385 m³

C
400 m³

D
1210 m³

Solution

Given: A rectangular sheet with dimensions 22 m × 10 m is rolled into a cylinder such that the smaller side becomes the height of the cylinder.
So, 2r = 22, where 'r' is the radius of the base of the cylinder.
r = m
h = 10 m = Height of the cylinder
Volume of the cylinder = r²h = × × × 10 = 11 × 7 × 5 = 385 m³
Question 20
1 / -0

A group of 25 people jumped into a swimming pool of a hotel for swimming. If the swimming pool is 30 m × 15 m and the average displacement of water by a person is 1.8 m³, then the rise in the water level in the pool will be

A
10 cm

B
15 cm

C
20 cm

D
25 cm

Solution

Displacement by one person = 1.8 m³
Total volume of water displaced by 25 people = 25 × 1.8 m³ = 45 m³
Therefore, rise in the water = (45/(30 × 15)) m = 0.1 m = 10 cm
Hence, answer option 1 is correct.
Question 21
1 / -0

A piece of metal pipe is 7 cm long with inner diameter of the cross section as 4 cm. If the outer diameter is 4.5 cm and the metal weighs 8 gm/cu. cm, then the weight of the pipe is

A
187 g

B
187 kg

C
1.87 kg

D
None of these

Solution

Weight of pipe (in grams) = Volume of pipe × 8

Volume of pipe = ; d_o = 4.5 cm, d_i = 4 cm, h = 7 cm

Volume of pipe = = 23.375 cm³
Weight per cu.cm = 8g
Weight of 23.375 cu.cm = 23.375 × 8 g = 187 g
Hence, answer option 1 is correct.
Question 22
1 / -0

In a trapezium, the shortest distance between the two parallel sides is 30 m and its area is 900 sq. m. If the ratio between the lengths of the parallel sides of the trapezium is 3 : 2, then find the sum of the lengths of the parallel sides.

A
45 m

B
60 m

C
70 m

D
85 m

Solution

Given: Area of the trapezium = 900 m²
Height = 30 m
We know,
Area of trapezium = (sum of parallel sides) height

Let the sum of parallel sides be 'x'.

900 =
x = 60 m

Question 23

1 / -0

Fill in the blanks and choose the correct answer with the help of the table given below.

(i) The lateral surface area of a cuboid becomes ______ times its original value if its length, breadth and height are doubled.
(ii) The volume of a cylinder becomes ______ times its original value if its radius is doubled and height is halved.
(iii) Opposite faces of a cuboid _____ equal in area.
(iv) In a rectangle, if the length (l) is halved and the breadth (b) is doubled, then the perimeter of the rectangle will be ______.

	(i)	(ii)	(iii)	(iv)
(A)	2	2	equal	l + 2b
(B)	3	3	unequal	2(l + b)
(C)	4	2	equal	l + 4b
(D)	2	3	unequal	4l + b

(A)

(B)

(C)

(D)

Solution

(i) Let the length, breadth and height of the cuboid be l, b and h, respectively.
Now,
Initial lateral surface area of a cuboid = 2h(l + b)
If length, breadth and height are doubled, then
New lateral surface area = 2(2h)(2l + 2b)
= 8h(l + b)
Therefore, the new lateral surface area will be 4 times the original lateral surface area.

(ii) Let the radius of the base and height of the cylinder be r and h, respectively.
Volume of a cylinder = r²h
After changing the values of radius and height as 2r and h/2, the new volume will be:
= 2πr²h
Therefore, the new volume is 2 times the original volume.

(iii) Opposite faces of a cuboid are equal in area.

(iv) Length of the rectangle = l
Breadth of the rectangle = b
Perimeter of the rectangle = 2(l + b)
After changing the values of length and breadth as l/2 and 2b, the new perimeter will be:
= l + 4b

Question 24

1 / -0

Match the following:

Column I	Column II
1. The surface area of a cube is 3456 cm². The volume of the cube (in cm³) will be	A. 300
2. The total distance (in m) covered by a girl if she takes a round of a regular heptagonal-shaped park of side 6 m is	B. 42
3. The percentage increase in the surface area of a cube when its edge length is doubled is	C. 13,824
4. The greatest number of cubes with each edge measuring 1 cm that can be cut from a cube with each edge measuring 8 cm is	D. 512

1 - A, 2 - B, 3 - C, 4 - D

1 - B, 2 - C, 3 - A, 4 - D

1 - C, 2 - B, 3 - A, 4 - D

1 - C, 2 - B, 3 - D, 4 - A

Solution

1. Surface area of the cube = 6(Side)² = 3456 cm²Side = 24 cm
Now, volume of the cube = 24 cm x 24 cm x 24 cm = 13,824 cm

2.
Perimeter = 7 × length of each side
= 7 × 6 = 42 m
Distance covered by the girl = 42 m

3. Let the edge length of the cube be x.
Surface area = 6x²
New edge length of the cube = 2x
Surface area = 6(2x)² = 24x²
Increase in area = 24x² – 6x² = 18x²
Percentage increase = = 300%
4.
Volume of the bigger cube = 8 cm × 8 cm × 8 cm = 512 cm³
Volume of the smaller cube = 1 cm × 1 cm × 1 cm = 1 cm³
Now, greatest number of cubes that can be cut from the given cube = = 512

Question 25
1 / -0

Water flows through a cylindrical pipe of inner diameter 7 cm at 192.5 litres per minute. Find (in kilometres per hour) the rate of flow of water. [1 litre = 1 cu. dm]

A
2 km/hr

B
3 km/hr

C
4 km/hr

D
5 km/hr

Solution

Radius = cm = dm, h = length of pipe

192.5 litres per minute = 192.5 dm³ per minute

Let the rate of flow (velocity) be R.
Water flow per hour = 192.5 x 60 dm³ = h
= 192.5 x 60 =

=

=

h = 30000 dm/hr

R = 30000 x km/hr

Rate of flow is 3 km per hour.

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Re-Attempt Weekly Quiz Competition

Mensuration Test - 7

Result

Mensuration Test - 7

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SHARING IS CARING

Question 1

6 cm

cm

cm

cm

Solution

Question 2

Solution

Question 3

=

b =

S1 = 2h( + b)

S2 = 2(b + bh + h)

Solution

Question 4

16 : 9

49 : 3

14 : 3

56 : 9

Solution

Question 5

256 cm3

512 cm3

1014 cm3

1024 cm3

Solution

Question 6

= 2p

Vp = q

= q

= q2

Solution

Question 7

600

1200

2400

4800

Solution

Question 8

30 + 6

30 + 10

30 + 4

30 + 12

Solution

Question 9

7 cm

9.8 cm

7.5 cm

49 cm

Solution

Question 10

21 m

20 m

60 m

70 m

Solution

Question 11

20 cm

30 cm

35 cm

40 cm

Solution

Question 12

1.25 m

2.5 m

3 m

50 m

Solution

Question 13

179.500 cm2

178.566 cm2

176.786 cm2

S₁ = 2h( + b)

S₂ = 2(b + bh + h)

256 cm³

512 cm³

1014 cm³

1024 cm³

= q²

^{_{30 + 6}}

^{_{30 + 10}}

179.500 cm²

178.566 cm²

176.786 cm²

176.468 cm²

365 m³

385 m³

400 m³

1210 m³