Question

If the dimensions of a cuboid are 30cm, 18cm and 24cm, then how many cubes of edge 6cm each can be cut out from it?​

Answer 1

Answer:

No. of cubes =

Volumeofsmallcube

Volumeofcuboid

​

=

4×4×4cm

3

20×18×16cm

3

​

=5×18=90cubes

Step-by-step explanation:

Answer 2

Answer:

• 60 cubes can be cut out from cuboid.

Explanation:

Given information,

If the dimensions of a cuboid are 30 cm, 18 cm and 24 cm, then how many cubes of edge 6 cm each can be cut out from it?

As dimensions (LBH) are given to us. So,

• Length of cuboid (L) = 30 cm
• Breadth of cuboid (B) = 18 cm
• Height of cuboid (H) = 24 cm
• Edge of each cube (a) = 6 cm

Using formula,

✪ Volume of cuboid = LBH ✪

Where,

• L = Length of cuboid
• B = Breadth of cuboid
• H = Height of cuboid

We have,

• L = 30 cm
• B = 18 cm
• H = 24 cm
• Volume of cuboid = ?

Putting all values,

➻ Volume of cuboid = (30)(18)(24)

➻ Volume of cuboid = 30 × 18 × 24

➻ Volume of cuboid = 540 × 24

➻ Volume of cuboid = 12960 cm³

• Hence, volume of cuboid is 12960 cm³.

Using formula,

✪ Volume of cube = a³ ✪

Where,

• a = edge of cube

We have,

• a = 6 cm
• Volume of cube = ?

Putting all values,

➻ Volume of cube = 6³

➻ Volume of cube = 6 × 6 × 6

➻ Volume of cube = 36 × 6

➻ Volume of cube = 216 cm³

• Hence, volume of cube is 216 cm³.

Now,

✪ Number of cubes to be cut out = (Volume of cuboid)/(Volume of cube) ✪

We have,

• Volume of cuboid = 12960 cm³
• Volume of cube = 216 cm³
• No. of cubes can be cut out = ?

Putting all values,

➻ No. of cubes = 12960/216

➻ No. of cubes = 60

• Hence, 60 cubes can be cut out from cuboid.

Important formulae,

↠ Volume of cube = a³

↠ Volume of cuboid = LBH

↠ Volume of cylinder = πr²h

↠ Volume of hollow cylinder = πh(R² - r²)

↠ Volume of cone = 1/3 πr²h

↠ Volume of sphere = 4/3 πr³

↠ Volume of hemisphere = 2/3 πr³

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