Question

a block of wood in the shape of cuboid has length= 2.5 metre, breadth=1.5 metre and height= 2 m.how many cubical blocks ,each of edge 50 cm can be cut from it?​

Answer 1

$\bold{\underline{\underline{Answer:}}}$

60 cubical blocks can be cut

$\bold{\underline{\underline{Step\:-\:by\:-\:step\:explanation:}}}$

Given :

• A cuboid shaped block,

1. Length = 2.5 m
2. Breadth = 1.5 m
3. Height = 2 m

• A cubical block,

1. Edge (s) = 50 cm

To find :

• Number of cubical block which can be cut from the cuboid block

Solution :

Covert the dimensions of cuboid block from 'm' to 'cm'

1 m = 100 cm

•°• Length (l) = 2.5 (100) = 250 cm

Breadth (b) = 1.5(100) = 150 cm

Height (h) = 2 (100) = 200 cm

Calculate the volume of the cuboid using the given dimensions.

The volume of cuboid is calculated using the formula :-

$\bold{\sf{\boxed{\red{Volume\:of\:a\:cuboid\:=\:l\times\:\:b\times\:h}}}}$

Block in the values,

$\rightarrow$$\bold{250\times\:150\times200}$

$\rightarrow$$\bold{250\times\:30000}$

$\rightarrow$$\bold{7500000}$

•°• Volume of cuboid = 7500000 cm³

Now, calculate the volume of the cube.

Formula :-

$\rightarrow$$\bold{\sf{\boxed{\red{Volume\:of\:a\:cube\:=\:s^3}}}}$

Block in the values,

$\rightarrow$$\bold{Volume\:of\:a\:cube\:=\:50^3}$

$\rightarrow$$\bold{Volume\:of\:a\:cube=\:50\times\:50\:\times\:50}$

$\rightarrow$$\bold{Volume\:of\:a\:cube\:=\:125000}$

•°• Volume of cube = 125000 cm³

Now to find the number of cubical blocks which can be cut from the cuboid block, simply divide the volume of cuboid by volume of cube.

Let the number of cubical blocks which can be cut be x,

x = $\bold{\frac{Volume\:of\:cuboid}{Volume\:of\:cone}}$

x = $\bold{\frac{7500000}{125000}}$

x = $\bold{\frac{7500}{125}}$

x = $\bold{60}$

•°• Number of cubical blocks which can be cut = 60