Test: Rotation of Shapes - Mechanical Engineering MCQ

1) For XYZZ

and ZZ

3) ZZZZ

The Dark Shaded edge is perpendicular to a given line and the Light shaded edge is parallel to the given line so it can be assumed that option 4 is correct but there is no sign of + represented anywhere in the Question.

Hence, the correct answer is "Option 4".

If we view the given figure from the direction of the arrow mentioned in the question we will see a trapezium on the right side placed above the rectangle.

option 1:

The above-given image will not be able to produce

The above-given image will be able to produce

as three triangles will make the bottom part whereas the remaining two will make the above part.

Option 3:

The above-given image will not be able to produce

as there is no scope for trapezium to fit in it.

Option 4:

The above-given image will not be able to produce

as one more triangle is required.

Thus option 2 is the correct  answer here.

Concept:

Area of an equilateral triangle  

where a = side of the triangle.

Calculation:

Given:

Let the side of the large triangle is 'a' then the side of the regular hexagon is a/3
If each triangle's area 
then the area of regular hexagon 

∴ The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is 2/3

Concept:
The volume of the solid cone 

Calculation:

Given:
A square sheet of side 1 unit is cut along the diagonal.

Now the triangle is revolved along its shortest length to form a solid cone 

where R = 1 unit, H = 1 unit.

The required volume of the resulting cone is:

For symmetry we have to add some squares

After combining the obtained figure we get 

Hence for making the P-Q line symmetry 6 squares must be added

let us consider a square sheet of side 1 unit.

Now fold the sheet along the main diagonal.

Now fold this along their line of symmetry.

again fold this along their line of symmetry.

The side of the resulting shape = 1/2 unit
 Area of resultant shape = 1/2 x side²

Area of resultant shape= 1/2 x 1/2 x 1/2

Area of resultant shape = 1/8

Given:

Two rectangular sheets M and N have the dimension 6 cm × 1 cm each,  in which cylinder will be formed by bringing the short edges of the sheet together. Given that ends of the cylinder are closed.

Concept:

Volume of cylinder = π x r2 x h
The volume of the cube = a³

Calculation:

Let be assume the side of the cube is a,
⇒ The area of the sheet N = 6 x a²
⇒ 6 × 1 = 6 x a²
⇒ a = 1
⇒ Volume of the cube = a³ = 1³ = 1
⇒  The circumference  = 6
⇒ 2 × π × r = 6, r = 3/π and height of the cylinder = 1 cm
⇒ Volume of the cylinder = π x (3/π)² x 1 = 9/π 
⇒ The required ratio = 9/π : 1
∴ The required result will be 9/π .