MCQ: Right Prism - SSC CGL MCQ

# MCQ: Right Prism - SSC CGL MCQ

Test Description

## 10 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: Right Prism

MCQ: Right Prism for SSC CGL 2024 is part of Quantitative Aptitude for SSC CGL preparation. The MCQ: Right Prism questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: Right Prism MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ: Right Prism below.
Solutions of MCQ: Right Prism questions in English are available as part of our Quantitative Aptitude for SSC CGL for SSC CGL & MCQ: Right Prism solutions in Hindi for Quantitative Aptitude for SSC CGL course. Download more important topics, notes, lectures and mock test series for SSC CGL Exam by signing up for free. Attempt MCQ: Right Prism | 10 questions in 15 minutes | Mock test for SSC CGL preparation | Free important questions MCQ to study Quantitative Aptitude for SSC CGL for SSC CGL Exam | Download free PDF with solutions
MCQ: Right Prism - Question 1

### The base of a prism is a right-angled isosceles triangle whose hypotenuse is 3√2 cm. If the height of the prism is 12 cm, find the volume of the prism?

Detailed Solution for MCQ: Right Prism - Question 1

Given:

Hypotenuse of base triangle = 3√2 cm

Height of prism = 12 cm

Formula used:

In a right angled triangle;

(Hypotenuse)2 = (Base)2 + (Height)

Area of triangle = (1/2) x Base x Height

Volume of Prism = Area of base x Height

Calculation:

In Isoceles triangle; two sides are equal.

Let the equal sides = a cm

(3√2)2 = a+ a2

⇒ 18 = 2a2

⇒ a2 = 9 cm2

⇒ a = 3 cm

Area of triangular base = (1/2) x 3 x 3

⇒ 9/2 cm2

Volume of Prism = 12 x (9/2) cm3

⇒ 54 cm3

∴ The volume of prism is 54 cm3.

MCQ: Right Prism - Question 2

### How many edges does a triangular pyramid have ?

Detailed Solution for MCQ: Right Prism - Question 2

A triangular pyramid has 6 edges

∴ The correct answer is 6

 1 Crore+ students have signed up on EduRev. Have you?
MCQ: Right Prism - Question 3

### A prism has a regular hexagonal base with side 12 cm. If the total surface area of prism is 1024√3 cm2, then what is the height (in cm) of prism?

Detailed Solution for MCQ: Right Prism - Question 3

Given:

A prism has a regular hexagonal base with side 12 cm.

Total surface area of prism = 1024√3 cm2

Formula used:

TSA of Prism = Base Perimeter × height + 2 x Base Area.

Area of hexagon = 3√3a2/2 . a = side

Total Area of hexagon Base = 2 × 3√3a2/2  = 3√3a2

Perimeter of hexagon = 6a

Concept used:

Surface area of regular hexagonal prism = 6ah + 3√3a2 (Where a = each side of the hexagon and h = height of the prism)

Calculation:

Let the height of the prism be h.

​According to the concept,

6 × 12h + 3√3 x 122 = 1024√3

⇒ 72h + 432√3 = 1024√3

⇒ 72h = 592√3

⇒ h = 592√3 ÷ 72

∴ The height of the prism is 74/3√3 cm.

MCQ: Right Prism - Question 4

The base of a right prism is an equilateral triangle whose side is 10 cm. If height of this prism is 10√3 cm, then what is the total surface area of prism ?

Detailed Solution for MCQ: Right Prism - Question 4

Given:

The base of a right prism is an equilateral triangle whose side is 10 cm.

Height of this prism is 10√3
Concept used:

TSA of Prism = [2(area of triangular base)] + [3(Area of rectangular sides)]

Area of Equilateral Triangle = (√3/4)a2

Area of rectangle = l × b

Calculation:

According to the concept,

⇒ Area of Equilateral Triangle = (√3/4)(10)2 = (100/4)√3 = 25√3

⇒ Area of rectangle = l × b = 10 × 10√3 = 100√3

Then,

TSA = [2(25√3)] + [3(100√3)]

⇒ TSA = 50√3 + 300√3

⇒ TSA = 350√3
∴ The total surface area of prism is 350√3.

MCQ: Right Prism - Question 5

The base of a right prism is a regular hexagon of a side 5 cm. If its height is 12√3 cm, then its volume (in cm3) is:

Detailed Solution for MCQ: Right Prism - Question 5

Given :-

The base of a right prism is a regular hexagon of side 5 cm

height is 12 √3 cm

Concept :-

Prism is a part of cylinder so,

Volume of prism = Base × Height

As base of prism is shan so

Volume of prism with base hexagonal = base area x height

Base area = Area of hexagonal is equal to area of 6 equilateral triangle = 6 x (√3/4) x side
Calculation :-

⇒ Base area = 6 x (√3/4) x 52

⇒ Base area = 150 x (√3/4)

⇒ Volume = 150 x (√3/4) x 12√3

⇒ Volume = (1800 x 3)/4

⇒ Volume = 1350 cm3

∴ Volume = 1350 cm3

MCQ: Right Prism - Question 6

What is the number of faces in a triangular prism?

Detailed Solution for MCQ: Right Prism - Question 6

Formula used:

Number of faces = Number of triangular bases + Number of lateral faces

Calculation:

According to question,

Number of faces = 2 (triangular bases) + 3 (lateral faces) = 5

∴ The correct answer is 5.

MCQ: Right Prism - Question 7

Find the surface area of a square prism with a 2 cm side and a 4 cm height.

Detailed Solution for MCQ: Right Prism - Question 7

Given :

Side of Square Prism = 2 cm
Height of Square Prism = 4 cm

Formula used :

Area  = 2 x side of square Prism + 4 x side of square Prism × height

Calculation :

Area = 2cm x 2cm + 4cm x 2cm x 4 cm
⇒ 40 cm

MCQ: Right Prism - Question 8

A prism has a regular hexagonal base with side 8 cm and the total surface area of the prism is 912√3 cm2, then what is the height of the prism?

Detailed Solution for MCQ: Right Prism - Question 8

Given:

The side of the prism = 8cm

The total surface area of the prism = 912√3 cm2

Formula used:

Area of the regular hexagon = 3√3/2 x side2

The total surface area of the prism = 2 × Area of the base + 6 × (Side of the base) × (Height of prism)

Calculation:

Let the height of the prism be h cm

Area of the regular hexagon = 3√3/2 x side2

⇒ 3√3/2 × 82

⇒ 96√3 cm2

The total surface area of the prism = 2 x Area of the base + 6 x (Side of the base) × (Height of prism)

⇒ 2 × 96√3 + 6 x 8 x h = 912√3

⇒ 6 x 8 x h = 720√3

⇒ h = 15√3

∴ The height of the prism is 15√3 cm

MCQ: Right Prism - Question 9

The lateral surface area of a right triangular prism is 288 cm2. If the lengths of the smaller bases are 6 cm and 8 cm respectively, find the height of the prism.

Detailed Solution for MCQ: Right Prism - Question 9

Length of the larger base = √(62 + 82) = 10 cm (Using Pythagoras theorem)

Let the length of the height of the prism be X cm.

Perimeter of the given prism = 6 cm + 8 cm + 10 cm = 24 cm

Area of the right triangular prism = Perimeter x Height

⇒ 24 x X = 288

⇒ X = 12 cm

MCQ: Right Prism - Question 10

The base of a right prism is a triangle whose sides are 8 cm, 15 cm and 17 cm, and its lateral surface area is 480 cm2. What is the volume (in cm3) of the prism?

Detailed Solution for MCQ: Right Prism - Question 10

Given:

The base of a right prism is a triangle whose sides are 8 cm, 15 cm and 17 cm

The lateral surface area of right prism 480 cm2

Formula Used:

Lateral surface area of prism = perimeter of base x height

Volume of prism = Area of base x height

Calculation:

Since base side length is 8, 15, 17 [which is a triplet]

It means the base is a right angled triangle

Perimeter of triangle = 8 + 15 + 17 = 40 cm

Let the height of the prime is h cm

So, 40 x h = 480

⇒ h = 12 cm

Now, Area of base = (1/2) x 8 x 15 = 60 cm2

Volume of prism = area x height

∴ Volume of prism = 60 x 12 = 720 cm3.

## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests
Information about MCQ: Right Prism Page
In this test you can find the Exam questions for MCQ: Right Prism solved & explained in the simplest way possible. Besides giving Questions and answers for MCQ: Right Prism, EduRev gives you an ample number of Online tests for practice

## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests