MCQ: Right Prism - SSC CGL MCQ

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)² 

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 = a² + 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.

A triangular pyramid has 6 edges 

∴ The correct answer is 6

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.

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.

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 side² 
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

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.

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

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

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

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.