Mensuration Test

Result

Mensuration Test - 11

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Weekly Quiz Competition

Question 1
1 / -0

If the volume of a cube is 1000 cm³, its total surface area is _____.

A
100 cm²

B
600 cm²

C
120 cm²

D
400 cm²

Solution

Volume of a cube = a³
1000= a³
a³ = 1000
a =
= 10 cm
Total surface area of cube = 6a²
= 6 (10)²
= 6 100
= 600 cm²
Question 2
1 / -0

The length and breadth of a cuboidal box are 3 cm and 5 cm, respectively. If its lateral surface area is 60 cm², the height of the box is

A
3 cm

B
3.75 cm

C
5 cm

D
7 cm

Solution

Length of cuboidal box = 3 cm
Breadth of cuboidal box = 5 cm
Lateral surface area = 2h ( + b)
60 = 2h (3 + 5)
60 = 2h (8)
= 8h
30 = 8h

h = 3.75 cm
Question 3
1 / -0

The volume of a cube with edge 6 m is _____.

A
144 m³

B
36 m³

C
18 m³

D
216 m³

Solution

Volume of cube = a³ ( `a` is the edge of the cube.)
Volume of cube = a³
= (6)³
= 6 6 6
= 216 m³
Question 4
1 / -0

The lateral surface area and height of a right circular cylinder are 88 cm² and 4 cm, respectively. Find the radius of its base.

A
1.75 cm

B
7 cm

C
14 cm

D
3.5 cm

Solution

Lateral surface area of the cylinder = 88 cm²
Height of the cylinder = 4 cm
Also, lateral surface area of the cylinder = 2rh
Therefore, 88 cm² = (2 r 4) cm
88 cm² = 2 cm
r = cm
= 3.5 cm
Question 5
1 / -0

The dimensions of a cuboidal box are 2 m 3 m 4 m. The lateral surface area of the box is equal to ______.

A
40 m²

B
36 m²

C
48 m²

D
52 m²

Solution

Lateral surface area = 2h ( + b)
= 2 4 (2 + 3)
= 8 (5)
= 40 m²
[ = 2m, b = 3m, h = 4m]
Question 6
1 / -0

The ratio of lateral surface area of a cube to its total surface area is

A
2 : 3

B
3 : 2

C
1 : 2

D
4 : 3

Solution

=
=
Ratio = 2 : 3
Question 7
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 8
1 / -0

If the length, breadth and total surface area of a cuboid are 3 cm, 4 cm and 94 cm² respectively, the height of the cuboid is equal to ______.

A
7 cm

B
cm

C
5 cm

D
cm

Solution

Length = 3 cm
Breadth = 4 cm
Total surface area = 2 (b + bh + h)
94 = 2 (12 + 4h + 3h)
= 12 + 7h
47 – 12 = 7 h
35 = 7 h
h = 5 cm
Question 9
1 / -0

The total surface area of a cube of edge 1.1 m is

A
1.21 m²

B
7.26 m²

C
13.2 m²

D
4.84 m²

Solution

Total surface area (TSA) of the cube = 6a², where 'a' is the edge of the cube.
TSA of the cube = 6 (1.1 m)²
= 6 1.21 m²
= 7.26 m²

Question 10

1 / -0

The edge of a cube of volume 512 cm³ is

6 cm

8 cm

cm

Solution

Volume of the cube = a³
512 = a³ a =
8 = a
a = 8 c

8	512
8	64
8	8
	1

Question 11
1 / -0

The total surface area of a cylinder with height 'a' and base radius 'b' is

A
2b (a + b)

B
2a (a + b)

C
2a²(a + b)

D
2ab

Solution

Total surface area of cylinder = 2r (r + h) ... (1)
'r' is the radius and 'h' is the height of the cylinder.
Given, radius = b
Height = a
Putting these in (1), we get
Total surface area = 2b (b + a)
or 2b (a + b)
Question 12
1 / -0

The length and height of a cuboidal box are 10 cm and 15 cm respectively. If its lateral surface area is 1200 cm², its breadth is equal to _____.

A
18 cm

B
45 cm

C
10 cm

D
30 cm

Solution

Given, length = 10 cm
Height = 15 cm
Lateral surface area = 1200 cm²
b = ?
We know, lateral surface area = 2h ( + b)
Therefore, 1200 = 2 15 (10 + b)
= (10 + b)
10 + b = 40
b = 40 – 10
= 30 cm
Question 13
1 / -0

If each edge of a cubical box is 3 m, its lateral surface area is ______.

A
54 m²

B
9 m²

C
36 m²

D
24 m²

Solution

Lateral surface area of a cubical box = 4a², where `a` is the edge of the box.
Given, a = 3 m
Lateral surface area = 4 (3)²
= 4 9
= 36 m²
Question 14
1 / -0

If the volume and the area of the base of a cuboidal tank are 375 cm³ and 75 cm² respectively, then its height is ______.

A
5 cm

B
cm

C
25 cm

D
cm

Solution

Area of base of cuboidal tank = b = 75 cm².
Volume of cuboidal tank = b h
375 = 75 h [ v = 375 cm³ (Given)]

h = 5 cm
Question 15
1 / -0

If the length, breadth and height of a cuboid are 6 cm, 8 cm and 7 cm respectively, the total surface area of the cuboid is equal to ______.

A
290 cm²

B
292 cm²

C
196 cm²

D
42 cm²

Solution

Given, Length of cuboid () = 6 cm
Breadth of cuboid (b) = 8 cm
Height of cuboid (h) = 7 cm
Total surface area of cuboid = 2 (b + bh + h)
= 2 (6 8 + 8 7 + 6 7)
= 2 (48 + 56 + 42)
= 2 (146)
= 292 cm²
Question 16
1 / -0

If the lateral surface area of a cube is 64 cm², its total surface area is equal to _____.

A
16 cm²

B
64 cm²

C
96 cm²

D
84 cm²

Solution

If `a` is the edge of the cube, then lateral surface area of cube = 4a²
64 = 4a²

16 = a²
a = 4 cm [ length is always positive]
Now, total surface area = 6 a²
= 6a²
= 6 (4)²
= 6 16
= 96 cm²
Question 17
1 / -0

If the total surface area of a cube is 96 cm², its volume is equal to _______.

A
16 cm³

B
12 cm³

C
64 cm³

D
192 cm³

Solution

If 'a' is the edge of the cube, then total surface area = 6a²
96 = 6a²
= a²
16 = a²
a = 4 cm [ length is always positive.]
Then volume = a³
= (4)³ = (4 4 4) cm³
= 64 cm³
Question 18
1 / -0

If A, r and h are the lateral surface area, radius of the base and height, respectively, of a cylinder, then which of the following relationships is true?

A
A = 4rh

B
A = 2r(r + h)

C
A = 2rh

D
A = r²h

Solution

Lateral surface area of cylinder = 2rh
A = 2rh
Question 19
1 / -0

If the volume and the radius of a cylinder are 41.58 cm³ and 2.1 cm respectively, the height of the cylinder is _______.

A
1.5 cm

B
3 cm

C
9 cm

D
1.732 cm

Solution

Given, radius of cylinder = 2.1 cm
Volume of cylinder = r²h
41.58 =
41.58 =
h =
h = 3 cm
Question 20
1 / -0

If the radius of the base and the height of a cylinder are 7 cm and 1 cm respectively, the volume of the cylinder is ______.

A
44 cm³

B
164 cm³

C
cm³

D
154 cm³

Solution

Given, radius of the base of cylinder = 7 cm
Height of the cylinder = 1 cm
Volume of the cylinder = r²h
=
=
=
= 154 cm³