MCQ: Cone - 2 - SSC CGL MCQ

# MCQ: Cone - 2 - SSC CGL MCQ

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## 10 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: Cone - 2

MCQ: Cone - 2 for SSC CGL 2024 is part of Quantitative Aptitude for SSC CGL preparation. The MCQ: Cone - 2 questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: Cone - 2 MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ: Cone - 2 below.
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MCQ: Cone - 2 - Question 1

### The slant height of a right circular cone is 13 cm, and the area of the base is 144π cm². Find the volume (in cm³) of the cone.

Detailed Solution for MCQ: Cone - 2 - Question 1

The slant height of a right circular cone is 13 cm and the area of the base is 144π cm2.

Concept used:

Volume of a cone = (π x R2 x H)/3
Slant height
where R = radius of the base, H = Height
The area of a circle = πR2 (R being the radius of the circle)

Calculation:

Let the radius of the base of the right circular cone be R cm.
According to the question,
πR2 = 144π
⇒ R2 = 122
⇒ R = 12 (since radius can't be negative)
Height of the right circular cone, H

⇒ 5 cm(since height can't be negative)

Now, the volume of the cone

⇒ (π x 122 x 5)/3

⇒ 240π cm3

∴ The volume of the cone is 240π cm3.

MCQ: Cone - 2 - Question 2

### Height and radius of a cone are 15 cm and 7 cm, respectively. What is the volume of the cone?

Detailed Solution for MCQ: Cone - 2 - Question 2

Volume of cone = πr2h/3

Volume of cone

⇒ [1/3] x π x r2 x h

⇒ [1/3] x [22/7] x 7 x 7 x 15

⇒ 22 x 7 x 5

⇒ 770 cm3

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MCQ: Cone - 2 - Question 3

### The circumference of the base of a 16 cm height solid cone is 33 cm. What is the volume of the cone in cm3?

Detailed Solution for MCQ: Cone - 2 - Question 3

Given

The circumference of the base = 33 cm
Height solid cone = 16 cm

Calculation:

Circumference of the base of a cone = 2πr

⇒ 2πr = 33

⇒ 2 x (22/7) × r = 33
⇒ r = 21/4

Volume of cone = (1/3) πr2h

⇒ (1/3) x (22/7) x (21/4) x (21/4) × 16

⇒ 21 x 22 = 462 cm3

∴ The volume of the cone is 462 cm3.

MCQ: Cone - 2 - Question 4

The curved surface area of a right circular cone of radius 28 cm is 4664 cm². What is the slant height of the cone? (Use π=22/7)

Detailed Solution for MCQ: Cone - 2 - Question 4

Given:

Curved surface area of a cone = 4664 cm2

Formula used:

Curved surface area of cone = π × r × l

where l = slant height; r = radius

Calculation:

Curved surface area = 4664
⇒ π × r × l = 4664
⇒ 22/7 × 28 × l = 4664
⇒ l = 53 cm
∴ Slant height i.e. l is 53 cm.

MCQ: Cone - 2 - Question 5

The slant height and radius of a cone are 30 cm and 14 cm, respectively. What is the total surface area of the cone?

Detailed Solution for MCQ: Cone - 2 - Question 5

Given:

Slant height of cone l = 30 cm

Radius of cone r = 14 cm

Formula:

Total surface area of cone = πr (l + r)

Calculation:

Total surface area of cone
⇒ πr(r + l)
⇒ [22/7] x 14 x (14 + 30)
⇒ 22 x 2 x 44
⇒ 1936 cm2

MCQ: Cone - 2 - Question 6

The height of the frustum of a cone is 8 cm. The radius on the top of the frustum is 6 cm and the bottom of the frustum is 12 cm. What is the curved surface area of the frustum?

Detailed Solution for MCQ: Cone - 2 - Question 6

Given:

Radius of the bottom of the frustum =  12 cm.
Radius of the top of the frustum = 6 cm.
Height = 8 cm

Formula used:
Slant Height of a Frustum of a cone,
Curved Surface Area of a Frustum of a cone, CSA = π × L(R + r)
Where Radius of the bottom of the frustum =  R, Radius of the top of the frustum = r, Height = H, and Slant Height = L

Calculation:
Hence, the slant height of a Frustum of a cone, L

Thus, the curved surface area of a Frustum of a cone, CSA
⇒ π x 10 x (12 + 6)
⇒ π x 10 x 18
⇒ 180π cm2

∴ The curved surface area of the frustum is 180π cm2.

MCQ: Cone - 2 - Question 7

The circumference of base of cone is 132 cm. The difference between the slant height and radius of base is 8 cm. Find the volume of cone.

Detailed Solution for MCQ: Cone - 2 - Question 7

Given,

Circumference of base of cone = 132
Radius of cone = 132 × 7/22 × 1/2 = 21 cm
Then,
Slant height of cone = 21 + 8 = 29 cm
Using Pythagoras theorem,
⇒ (Slant height)2 = (Height)2 + (Radius)2
⇒ Height2 = 292 – 212
⇒ Height = 20 cm
Volume of cone = 1/3 × πr2h
= 1/3 × 22/7 × 21 × 21 × 20
= 9240 cm3

MCQ: Cone - 2 - Question 8

The height and the slant height of a right circular cone are given as 3√23 cm and 16 cm respectively. Approximating π by 22/7, find the curved surface area of the same cone.

Detailed Solution for MCQ: Cone - 2 - Question 8

Formula of curved surface area of a cone = πrl

where r is the radius and l is the slant height of cone.

⇒ r = √(l2 – h2)

⇒ r = √(256 – 207)

⇒ r = √49 = 7 cm

∴ Curved surface area of the cone = (22/7)x 7 x 16 = 352 cm2

MCQ: Cone - 2 - Question 9

A glass container is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 6 cm and 4 cm. Find the capacity of the container.

Detailed Solution for MCQ: Cone - 2 - Question 9

Formula used:

Volume of frustum of cone

Where r1 and r2 are radius of the frustum of cone

Given:

Radius (r1) of the upper base = 6/2 = 3 cm

Radius (r2) of lower the base = 4/2 = 2 cm

Height = 14 cm

Calculation:

∴ The capacity of the glass = 88.67π cm3

MCQ: Cone - 2 - Question 10

The frustum of a right circular cone has the radius of the base as 5 cm, radius of the top as 3 cm, and height as 6 cm. What is its volume?

Detailed Solution for MCQ: Cone - 2 - Question 10

Given:

Radius of the base (R) = 5 cm
Radius of the top (r) = 3 cm
Height (H) of frustum = 6 cm

Formula used:

Volume of Frustum (V) = 1/3 πH (R2 + Rr + r2)

Calculations:

According to the question,

Volume of Frustum = 1/3 π × 6 × [(5)2 + (5 × 3) + (3)2]
⇒ V = π x2 x [25 + 15 + 9]
⇒ V = π x 2 x [49] = 98π cm3
∴ The volume of frustum is 98π cm3

## Quantitative Aptitude for SSC CGL

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## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests