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There is an ample supply of identical blocks (as shown). Each block is constructed from four 1 × 1 × 1 unit-cubes glued whole-face to whole-face. What is the greatest number of such blocks that can be packed into a box that is 6 units tall, 7 units wide, and 8 units deep without exceeding the height of the box?

There is an ample supply of identical blocks as shown Each block is constructed from four 1 1 1 unitcubes glued wholeface to wholeface What is the greatest numb class=

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Answer: 72

Step-by-step explanation: We did this question during class and this was the answer. Hope this helps!

dwivedisiddhant03

The number of block that can be placed in box can be calculated by finding the area of the ample supply of identical blocks.

The number of block that can be placed in block is 84.

Given:

The box is 6 units tall, 7 units wide, and 8 units deep.

Calculate the area of the box.

[tex]\begin{aligned}{\rm Area\: of\:the\: box}=6\times7\times 8\\=336\:\rm units\\\end[/tex]

The four block has [tex]1\times1\times1[/tex] unit-cubes.

Calculate the area of 4 block.

[tex]\begin{aligned}{\rm Area\:of\:four\:block}&=4\times1\times1\times1\\&=4\\\end[/tex]

Now, calculate the number of block that can be placed,

[tex]\begin{aligend}{\rm Block\: placed\: in \:box}&=\dfrac {\rm Area\: of\: box}{\rm Area \:of\: Block}\\&=\dfrac{336}{4}\\&=84\\\end{aligned}[/tex]

Thus, the number of block that can be placed in block is 84.

Learn more about area here:

https://brainly.com/question/25632432

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