Mensuration Test

Result

Mensuration Test - 10

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Weekly Quiz Competition

Question 1

1 / -0

The volume of a cubical box is 343 cm³. Its lateral surface area is

1372 cm²

56 cm²

196 cm²

294 cm²

Solution

Volume of the cubical box = 343 cm³
a³ = 343 cm³
Taking cube root, we get

7	343
7	49
7	7
	1

a =
=
a = 7 cm
Now, lateral surface area (LSA) of the cube = 4a²
= 4 (7)²
= 4 (7 7)
= 4 49
= 196 cm²

Question 2
1 / -0

What is the volume of a cube with an edge length of 2 units?

A
cubic units

B
cubic units

C
cubic units

D
cubic units

Solution

Edge of the cube = units
Volume of the cube = units units units = cubic units
Question 3
1 / -0

The curved surface area and the base radius of a right circular cylinder are 4.4 cm² and 0.7 cm, respectively. Find the height of the cylinder.

A
2 cm

B
10 cm

C
0.5 cm

D
1 cm

Solution

Surface area of the cylinder = 4.4 cm²
Radius of the cylinder = 0.7 cm
Height of the cylinder = ?
Curved surface area of the cylinder = 2rh
4.4 = 2

h = 1 cm
Question 4
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 5
1 / -0

The dimensions of a cuboidal tank are 10 m 5 m 9 m. What is its volume?

A
450 m³

B
270 m³

C
350 m³

D
370 m³

Solution

Volume of the cuboidal tank =
= length of the tank
b = breadth of the tank
h = height of the tank
Volume of the tank = 10 5 9 m³
= 450 m³
Question 6
1 / -0

If the length, breadth, height and total surface area of a cuboid are , b, h and S, respectively, then which of the following relationships is true?

A
S = 2[b + bh + h]

B
S = 2[b - bh + h]

C
S = 2[h + bh - b]

D
S = 2h( + b)

Solution

Surface area of a cuboid is equal to the sum of areas of all its faces.
All the six faces of a cuboid are rectangular in shape.
Area of front face = length breadth
= h [ h is the breadth of the front face]
= h
Similarly, area of back face = h
Area of left face = h b = hb
Area of right face = hb = hb
Area of top face = b
Area of bottom face = b
Now,
Surface area of cuboid = Sum of area of all the six faces
= h + h + hb + hb + b + b
= 2h + 2hb + 2b
= 2(h + hb + b)
Question 7
1 / -0

If the volume of a cube is (12)³ m³, then the total surface area of the cube is equal to

A
144 m²

B
576 m²

C
432 m²

D
864 m²

Solution

Volume of a cube = a³, where 'a' is the edge of the cube.
Given, volume of the cube = (12)³ m³
a³ = (12)³ m³
Taking cube root, we get
a = 12 m
Now, total surface area of the cube = 6a²
= 6(12)²
= 6 12 12
= 6 144
= 864 m²
Question 8
1 / -0

The length and the breadth of a cuboidal box are 2 m and 0.5 m, respectively. If the lateral surface area of the box is 7.5 m², its height is

A
1.1 m

B
1.5 m

C
5.5 m

D
3.75 m

Solution

Lateral surface area of the cuboid = 2h( + b)
h = Height of the cuboid
b = Breadth of the cuboid
= Length of the cuboid
Given: = 2 m, b = 0.5 m, h = ?
Lateral surface area of the cuboid = 7.5 m²(Given)
Therefore, 7.5 = 2h(2 + 0.5)

= h
h =
=
= 1.5
Thus, the height of the box is 1.5 m.
Hence, answer option 2 is correct.
Question 9
1 / -0

The base radius and volume of a right circular cylinder are 3 m and 198 m³, respectively. What is its height?

A
10.5 m

B
7 m

C
21 m

D
m

Solution

Volume of a cylinder = r²h …………. (1)
Where,
π =
r = base radius of the cylinder
h = height of the cylinder
Given: Volume of the cylinder = 198 m³
Radius of the cylinder = 3 m
Height of the cylinder = ?
Thus, 198= (3)²h
198 = [∵ (3)² = 3 3 = 9]
h = 7 m
Question 10
1 / -0

The volume and height of a right circular cylinder are 34650 cm³ and 25 cm, respectively. The diameter of its base is

A
20 cm

B
21 cm

C
41 cm

D
42 cm

Solution

Volume of cylinder = r²h
34650 = (r²) 25 (Given)
34650 =

441 = r²
r =
r =
r = 21 cm
Now, diameter = 2 r
= 2 21 cm
= 42 cm
Question 11
1 / -0

If the total surface area of a cube is 54 m², then its lateral surface area is equal to

A
81 m²

B
24 m²

C
36 m²

D
108 m²

Solution

Total surface area of the cube = 6a²
54 m²= 6a²m² = a²
9 m²= a²
a = 3m [ Length cannot be negative.]
Now, lateral surface area of the cube = 4a²
= 4 (3)²m²
= 4 3 3 m²
= 36 m²
Question 12
1 / -0

The length and breadth of a cuboidal box are equal. Its height is 6 cm and lateral surface area is 120 cm². The volume of the box is

A
180 cm³

B
600 cm³

C
150 cm³

D
60 cm³

Solution

Given: = b
h = 6 cm
Lateral surface area = 120 cm²(Given)
Lateral surface area (LSA) of the box = 2h ( + b)
120 = 2 6 (2)

10 = 2
= = 5 cm
= b = 5 cm
Volume of the box = b h
= 5 5 6
= 25 6
= 150 cm³
Question 13
1 / -0

If the length, height and total surface area of a cuboid are 11 cm, 6 cm and 404 cm², then the breadth of the cuboid is equal to

A
cm

B
cm

C
cm

D
cm

Solution

= 11 cm, h = 6 cm, b = ?
Total surface area = 2(b + bh + h)
404 = 2(11b + 6b + 66)
404 = 2(17b + 66)
202 = 17b + 66
202 – 66 = 17b
136 = 17b

Thus, b = cm
Question 14
1 / -0

If each edge of a cube is 'a', then its total surface area is

A
3a²

B
6a²

C
4a²

D
a²

Solution

Each edge of the cube = a
Total surface area of the cube = Sum of areas of all the faces of the cube
All the 6 faces of the cube are of the same dimension.
Area of top face = (side)² = a²
Area of bottom face = a²
Area of left face = a²
Area of right face = a²
Area of front face = a²
Area of back face = a²
Total surface area = a² + a² + a² + a² + a² + a² = 6a²
Question 15
1 / -0

The length, breadth and height of a cuboidal tank are 1.5 m, 1.2 m and 1 m, respectively. The lateral surface area of the tank is equal to

A
9 m²

B
5.4 m²

C
6 m²

D
6.6 m²

Solution

Lateral surface area of the tank = 2h( + b)
= 2 1 [1.5 + 1.2] m² (Given: = 1.5 m, b = 1.2 m and h = 1 m)
= 2 (2.7) m²
= 5.4 m²
Question 16
1 / -0

If the volume of a cubical box is 343 cm³, what is the length of its edge?

A
cm

B
cm

C
cm

D
7 cm

Solution

If 'a' is the edge of a cube, then volume of the cube = a³
Therefore, 343 cm³ = a³
Taking cube root on both sides, we get
a = 7 cm
Question 17
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 18
1 / -0

Find the lateral surface area of a cube of edge 10 cm.

A
400 cm²

B
80 cm²

C
600 cm²

D
100 cm²

Solution

Lateral surface area (LSA) of a cube = 4a² (where 'a' is the edge of the cube)
LSA of the given cube = 4(10 cm)²
= 4(100) cm²
= 400 cm²
Question 19
1 / -0

The area of the base of a cuboidal box is 56 cm². If the height of the box is 5 cm, the volume of the box is equal to _____.

A
560 cm³

B
280 cm³

C
61 cm³

D
300 cm³

Solution

Area of base of a cuboidal box = b
56 = b [ Base of a cuboidal box is a rectangle with dimensions and b.]
Given, height = 5 cm
Volume of cuboidal box = b h
= 56 5
= 280 cm³
Question 20
1 / -0

If the breadth, height and total surface area of a cuboid are 4 cm, 4 cm and 80 cm² respectively, the length of the cuboid is equal to ____.

A
3 cm

B
5 cm

C
6 cm

D
7 cm

Solution

Total surface area = lb+lh+bhso,40 = 8 + 16
40 – 16 = 8
=
3 =
= 3 cm