Mensuration Test - 1

- Volume Formula: Volume = Length ×Breadth ×Height
- Given Dimensions:
- Length = 8 cm
- Breadth = 6 cm
- Height = 3.5 cm
- Substituting the given values:
- 8 ×6  ×3.5
- 48 ×3.5 = 168
- Result: The volume of the cuboid is 168 cm ³ .

Volume of cubiod =l×b×h
=8×3×5
=120cm3 .

Because the perimeter of square is 4×side
so, 4×4=16

Area of the circle=πr²

2464 = 22/7 * r²

Radius of the circle=28  cm

Circumference of the circle=2 * π* r =2 * 22/7 * 28  

= 176  cm

Breadth of the rectangle=6/7  * 28=24  cm

Perimeter of the rectangle=2 * (l + b)

176 = 2 * (l + 24)

Length of the rectangle = 64  cm

Area of the rectangle = l * b = 24  * 64 = 1536  cm²  

use formula:1/2(sum of of parallel sides)(distance between them)

Area = Base x Height = 10 x 2 = 2 cm²  .

The total surface of a cube is calculated using the formula: Total Surface Area = 6 x (side length)²

Edge of the cube = 1 cm

substitute the value into the formula: Total Surface Area = 6 x 1  ²  = 6 cm²

We know that area of triangle is equals to 1/2 base ×altitude.
Here, base = 4 cm and altitude = 6 cm.
So, area = 1/2 ×4 ×6= 24 /2= 12 cm² .

Let the length of one diagonal be d₁ = 20  cm, and the length of the other diagonal be d₂

The formula for the area of a rhombus is:
Area = 1/2 x  d₁   x  d ₂

Substitute the given values:

200 cm ²= 1/2 x 20  x  d₂

200 cm ²= 10  x  d₂

20cm = d₂  

Given:  
The length of each side of a cube is 24 cm.  
The breadth and the height of the cuboid are 32 cm and 12 cm, respectively.  

Concept used:  
The volume of the cube is equal to the volume of a cuboid.  
Volume of cube = a ³ 
Volume of cuboid = lbh  

Calculation:  
The volume of the cube is equal to the volume of a cuboid.  
⇒24 ³= l ×32 ×12  
⇒l = 3 ×12  
⇒l = 36  

∴Option 1 is the correct answer.