Question

How many 3cm blocks can you put inside a 6cm by 9cm by 27cm wooden box

Answer 1

Wooden box ( Cuboid )-

Length = 6cm

Breadth= 9cm

Height = 27cm

Volume of the cuboid =

$lbh = 6 \times 9 \times 27 = 1458cm {}^{3}$

Block( Cube)-

Side = 3cm

Volume of cube =

${s}^{3} = {3}^{3} = 27cm {}^{3}$

No. of blocks that can be put inside the wooden box =

$volume \: of \: wooden \: box(cuboid) \div volume \: of \: block(cube)$

$= 1458 \div 27 = 54 \: blocks$

This is your answer. Hope it helps.

Answer 2

Answer:

The number of blocks that can be put inside a wooden box is 54.

Step-by-step explanation:

Given : block of size 3cm, wooden box of length =6cm, breadth = 9cm and height = 27cm.

To find: the number blocks that can be put inside the wooden box.

Solution: the given wooden box have length, breadth and height.so it is a cuboid.

Also the block has measure 3cm ,it is a cube.

A cube is a three -dimensional solid object bounded by six square faces, with three meeting at each vertex. It has 6 faces, 12 edges and 8 vertices.

A cuboid is a three-dimensional solid shape that has 6 faces, 8 vertices , and 12 edges. The three dimensions of a cuboid are its length, width, and height.

It is different from a cube since all the faces of a cuboid are rectangular in shape, whereas, a cube has square faces.

first we will find the volume of cube and cuboid.

Volume of cube = side ×side ×side

Volume of block (cube) = a³ = 3³ = 3×3×3 =  27cm³.

Volume of wooden box (cuboid) = l ×b × h

                                                       =6 ×9 ×27 = 1458cm³.

The number of blocks that can be put inside the wooden box

= Volume of wooden box = 1458÷ 27 = 54.

     Volume of block    

∴ The number of blocks that can be kept inside a wooden box is 54.

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