MCQ: Sphere - SSC CGL MCQ

# MCQ: Sphere - SSC CGL MCQ

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## 15 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: Sphere

MCQ: Sphere for SSC CGL 2024 is part of Quantitative Aptitude for SSC CGL preparation. The MCQ: Sphere questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: Sphere MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ: Sphere below.
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MCQ: Sphere - Question 1

### The length of the side of a cube is 5.6 cm. What is the volume of the largest sphere that can be taken out of the cube?

Detailed Solution for MCQ: Sphere - Question 1

Given:

Edge of the cube = 5.6 cm

Formula used:

The volume of the sphere = (4/3) × π × r3

Calculation:

Diameter of the sphere = Edge of the cube
⇒ 2 × radius of sphere = 5.6 cm
⇒ The radius of sphere = 5.6/2 = 2.8 cm
The volume of the sphere = (4/3) × (22/7) × (2.8)3
⇒ 88/21 × 21.952
⇒ 91.98
∴ The volume of the largest sphere that can be taken out of the cube is 91.98 cm3

MCQ: Sphere - Question 2

### If three solid gold spherical beads of radii 6 cm, 8 cm, and 10 cm, respectively are melted into one spherical bead, then what is the radius (in cm) of the larger bead?

Detailed Solution for MCQ: Sphere - Question 2

Given:

Spheres of radius r1 = 6 cm, r2 = 8 cm, r3 = 10 cm molten in single one.

Formula used:

The volume of Sphere = 4/3π r3

Calculations:

According to the question,
⇒ 4/3π [(6)3 + (8)3 + (10)3] = 4/3π R3
⇒ R3 = [(216) + (512) + (1000)]
⇒ R3 = 1728 = 12 cm.
∴ The radius (in cm) of the larger bead will be 12 cm.

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MCQ: Sphere - Question 3

### A sphere has a radius of 8 cm. A solid cylinder has a base radius of 4 cm and a height of h cm. If the total surface area of the cylinder is half the surface area of the sphere, then find the height of the cylinder.

Detailed Solution for MCQ: Sphere - Question 3

Given:

Radius of sphere = 8 cm
Radius of cylinder = 4 cm
The total surface area of the cylinder is half the surface area of the sphere

Formula used:

Total surface area of cylinder = 2πr(h + r)
Surface area of sphere = 4πr2

Calculation:

According to the question
The total surface area of the cylinder is half the surface area of the sphere

∴ The height of the cylinder is 12 cm

MCQ: Sphere - Question 4

A metallic solid cuboid of sides 44 cm, 32 cm and 36 cm melted and converted into some number of spheres of radius 12 cm. How many such sphere can be made with the metal (π = 22/7)?

Detailed Solution for MCQ: Sphere - Question 4

Given:

The sides of the cuboid are 44 cm, 32 cm, and 36 cm
The radius of the sphere is 12 cm

Concept Used:

The volume of a cuboid of sides l, b and h = l x b x h
The volume of the sphere of radius r = (4/3)πr3

Calculation:

The volume of the metallic cuboid is (44 x 32 x 36) cm3
The volume of the sphere is (4/3) x π x 123
Let, the total number of such sphere is n
Accordingly,

∴ Such 7 spheres can be made by given metallic cuboid.

MCQ: Sphere - Question 5

If the surface area of a sphere is 64 π cm2, then the volume of the sphere is:

Detailed Solution for MCQ: Sphere - Question 5

GIVEN:

The surface area of a sphere = 64π cm2

FORMULA USED:

The surface area of a sphere = 4πr2
The volume of a sphere = 4πr3/3

CALCULATION:

The surface area of a sphere = 64π
⇒ 4πr2 = 64π
⇒ r2 = 16
⇒ r = 4cm

MCQ: Sphere - Question 6

A copper sphere of diameter 18 cm is drawn into a wire of diameter 6 mm. Find the length of the wire.

Detailed Solution for MCQ: Sphere - Question 6

Given:

A copper sphere of diameter 18 cm is drawn into a wire of diameter 6 mm.

Concept used:

Volume of sphere = 4/3πr3
Volume of cylinder = πr2h

Calculation:
Radius of sphere = 9 cm
Radius of wire = 0.3 cm  [As 1 cm = 10 mm]
According to the question,
Volume of sphere = Volume of cylinder

∴ The length of the wire is 108 m.

MCQ: Sphere - Question 7

If the surface area of a sphere is 1386 cm2, then find the radius of the sphere.

Detailed Solution for MCQ: Sphere - Question 7

GIVEN:

The surface area of a sphere = 1386 cm2

FORMULA USED:

The surface area of a sphere = 4πrwhere r is the radius of the sphere.

CALCULATION:

The surface area of a sphere =4πr2 = 1386

∴ The radius of the sphere is 10.5 cm.

MCQ: Sphere - Question 8

If the diameter of a sphere is doubled, how does its surface area change?

Detailed Solution for MCQ: Sphere - Question 8

Formula used:

Area of Sphere = 4πr2
Here,

Calculation:

It is given that, the diameter of a sphere is doubled so its radius will also get doubled.
Let the initial and final radius of sphere be r and R.

Now change in surface area = 4A - A = 3A

∴ Its surface area will increase three times.

MCQ: Sphere - Question 9

A hemisphere of lead of radius 4 cm is cast into a right circular cone of height 72 cm. What is the radius of the base of the cone?

Detailed Solution for MCQ: Sphere - Question 9

Given:

A hemisphere of lead of radius 4 cm is cast into a right circular cone of height 72 cm.

Concept used:

3. The volume of the hemisphere must be equal to the volume of the cone.

Calculation:

The volume of the hemisphere

Let the radius of the base of the right circular cone be R cm.

​According to the concept,

∴ The radius of the base of the cone is 1.33 cm.

MCQ: Sphere - Question 10

The volume of a solid spherical ball was 972πcm3. It was melted and 27 identical spheres were made with the molten material, leaving no wastage. What is the total surface area of the 27 smaller spheres taken together?

Detailed Solution for MCQ: Sphere - Question 10

Given:
The volume of a solid spherical ball (V1) = 972π cm2

Formula used:
The volume of the sphere = 4/3πr3
The total surface area of the sphere = 4πr2

Calculations:
According to the question,
It was melted into 27 smaller spheres of radius r and Volumes (V2)
V1 = V2

Now, the total surface area of 27 spheres:

∴ The total surface area of the 27 smaller spheres taken together will be 972π cm².

MCQ: Sphere - Question 11

A spherical metallic ball S of radius 9 cm. If the bigger metallic spherical ball S is melted and recast into N number of smaller spherical balls of radius 3 cm, then find the value of N.

Detailed Solution for MCQ: Sphere - Question 11

Given:

A metallic spherical ball S of radius 9 cm.
The metallic spherical ball S is melted and recast into N number of spherical balls of radius 3 cm.

Concept used:

The formula of the sphere:

Where,

R, is the radius of the sphere

Calculation:

The radius of bigger metallic sphere S, R = 9 cm
The radius of the smaller metallic sphere, r = 3 cm
Let N be the number of smaller spheres.
Let VB and VS be the volume of bigger and smaller spheres.
According to the question,

∴ The required number of smaller spheres is 27.

MCQ: Sphere - Question 12

A hollow sphere has an outer radius of 4 cm and inner radius of 1 cm. What is the volume of this hollow sphere?

Detailed Solution for MCQ: Sphere - Question 12

Given:

For hollow sphere,
Outer radius (ro) = 4 cm.
Inner radius (ri) = 1 cm.

Concept used:
Volume of hollow sphere

Calculation:

Volume of hollow sphere = (4/3)p x (43 - 13)
⇒ (4/3)p x (64 - 1)

⇒ (4/3)px 63

⇒ 84p

∴ The volume of the hollow sphere is 84p cm3.

MCQ: Sphere - Question 13

0.1 per cent of 1.728 x 106 spherical droplets of water, each of diameter 2 mm, coalesce to form a spherical bubble. What is the diameter (in cm) of the bubble?

Detailed Solution for MCQ: Sphere - Question 13

Concept used:

• Sum of the volumes of small droplets = volume of the big droplet
• Volume of sphere = 4/3 x π x r3

Calculation:

Total number of small droplets are  0.1% of 1.728 x 106 = 1728

Let the radius of big bubble be R mm
⇒ 1728 x 4/3 x π x (2/2)3 = 4/3 × π × R3
⇒ R3 = 1728
⇒ R = 12 mm or 1.2 cm
Then diameter is 2 × 1.2 = 2.4 cm
∴ The correct answer is 2.4 cm

MCQ: Sphere - Question 14

When the radius of a sphere is increased by 5 cm, its surface area increases by 4840/7 cm2. What is the volume (in cm3) of the original sphere? (Take π = 22/7, nearest to an integer)

Detailed Solution for MCQ: Sphere - Question 14

Given:

The surface area increased by 4840/7 cm2 by the increase of the radius 5 cm

Formula used:

A = 4 x π x R2     Where, V = Volume of the sphere, A = Surface area of the sphere and R = Radius of the sphere

Calculation:

Let the radius of the sphere be R

According to the question

The volume of the sphere

= 113.14 ≈ 113 cm3

MCQ: Sphere - Question 15

A solid cone of radius 7 cm and height 7 cm was melted along with two solid spheres of radius 7 cm each to form a solid cylinder of radius 7 cm. What is the curved surface area (in cm2) of the cylinder? (Use π = 22/7)

Detailed Solution for MCQ: Sphere - Question 15

Given:

A solid cone of radius 7 cm and height 7 cm was melted along with two solid spheres of radius 7 cm each to form a solid cylinder of radius 7 cm.

Formula used:

The volume of a cone = 1/3πr2h
Volume of a cylinder = πr2h
The volume of a sphere = 4/3πr3
The curved surface area of a cylinder = 2πrh
Here,
h = height

Calculation:

The volume of the cone = 1/3π × 72 × 7
⇒ 1/3π x 73

The volume of each sphere = 4/3π × 73
Let the height of the formed cylinder be H
According to the question,

So, the height of the formed cylinder is 21 cm
Now,
The curved surface area of the cylinder = 2 x 22/7 x 7 x 21
⇒ 924
∴ The curved surface area (in cm2) of the cylinder is 924.

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