Question

how many cuboids of sides 6 cm, 3cm, 6cm will be needed to form a cube of side 6 cm​

Answer 1

Answer:

Then the number of cuboids is: 216/108=2 Ans

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Answer 2

Given:

• How many cuboids of sides 6 cm, 3cm, 6cm will be needed to form a cube of side 6 cm?

Formula used:

• Length × Breadth × Height

Understanding the Question:

• First we have to find the volume of one cuboid and then the volume of the total cuboid and then the volume of the cube.

Solution:

• Let the length be 6 cm

• Let the breadth be 3 cm

• Let the height be 6 cm

$\\ { \therefore \sf \: \: \: \: Volume \: of \: one \: cuboid = l \times b \times h} \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 6 \times 3 \times 6 \: {cm}^{3} \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 108 \: {cm}^{3}$

Now, Let the total cuboid be x.

$\\ { \therefore \sf \: \: \: \: Volume \: of \: total \: cuboid = x \times 108 \: {cm}^{3}} \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \ \: = 108x \: {cm}^{3}$

$\\ \sf { Now, \sf \: \: \: \: Volume \: of \: the \: cube = 6 {}^{3}}\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 216 \: {cm}^{3}$

Hence, ⠀⠀⠀108x = 216

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x = 216/108

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀x = 2