a metal block of length 4cm,breadth3cm and height2.5cm weighs 500g.what is the mass of a block of length5cm,breadth4cm,and height3cm made of same metal
Solve it
Volume of a metal block of length 4 cm, breadth 3 cm and height 2.5 cm
V = L ∙ B ∙ H
V = 4 ∙ 3 ∙ 2.5 = 30 cm³
mass = 500 g
Density :
ρ = m / V = 500 / 30 = 10 ∙ 50 / 10 ∙ 3 = 50 / 3 ( g / cm³ )
Volumea block of length 5cm , breadth 4c m,a nd height 3 cm:
V1 = 5 ∙ 4 ∙ 3 = 60 cm³
m1 = V1 ∙ ρ = 60 ∙ 50 / 3 = 3 ∙ 20 ∙ 50 / 3 = 20 ∙ 50 = 1000 g
OR
V1 / V = 60 cm³ / 30 cm³ = 2
Mass is directly proportional to the volume.
A body with double volume made of the same material has a double mass.
m1 = 2 ∙ m = 2 ∙ 500 = 1000 g
To find the mass of a block with different dimensions but made of the same metal, we need to understand the relationship between mass and volume.
The density of a material is defined as the mass per unit volume. In this case, since we have two blocks made of the same metal, we can assume that they have the same density.
The formula to calculate the volume of a rectangular prism (or a block) is:
Volume = length x breadth x height
For the first block, its volume is:
Volume1 = 4cm x 3cm x 2.5cm
To calculate the volume in cubic centimeters (cm³), we multiply the dimensions together:
Volume1 = 30 cm³
Now, let's calculate the density of the first block. We know that:
Mass1 = 500g
Since density = mass/volume, we can rearrange the formula to find the density:
Density1 = Mass1 / Volume1
Density1 = 500g / 30 cm³
Density1 ≈ 16.67 g/cm³
Now, let's use the density to find the mass of the second block:
Since density = mass/volume, we can rearrange the formula to find the mass:
Mass2 = Density1 x Volume2
First, calculate the volume of the second block:
Volume2 = 5cm x 4cm x 3cm
Volume2 = 60 cm³
Finally, we can calculate the mass of the second block:
Mass2 = Density1 x Volume2
Mass2 = 16.67 g/cm³ x 60 cm³
Mass2 ≈ 1000 g
Therefore, the mass of the block with dimensions of length 5cm, breadth 4cm, and height 3cm, made of the same metal, is approximately 1000 g.