Math, asked by hashimiqbal345gd, 10 months ago

Jun Wei has a paper box with a length of 8 m, a breadth of 12 m and a height of 16 m.
(a) He is thinking of packing small cubes into the box. If each small cube is of length 2 m, what is the number
of small cubes that he is able to pack into the box?
length of the cube such that the cubes can fill the box entirely.
(b) On the other hand, Jun Wei wants to pack cubes of a larger size into the box. Find the greatest possible

Answers

Answered by Anonymous

Given,

Length of the box = 8 metres

Width of the box = 12 metres

Height of the box = 16 metres

Length of the side of the smaller cube = 2 metres

i) For, calculating the total number of smaller cubes that can be packed into the box,we have to calculate the volume of both the bigger box and one smaller cube.

Volume of the box = length × width × height = (8×12×16)m³

= 1536 m³

Volume of the smaller cube = (side)³ = (2)³ m³ = 8 m³

So,the number of smaller cubes that can be packed in the box is = volume of box/volume of one cube = 1536/8 = 192

Hence,192 smaller cubes can be packed in the box.

ii) For calculating,the length of the side of the largest cubes,that can be fitted into the box we need to divide the total volume of the box by the whole numbers (1,2,3,4,5.....so on). Then we have to note down the value of quotient of each of the divisions. The first quotient which is a perfect cube,will be the volume of the largest cubes.

So,

1536 ÷ 1 = 1536 (not a cube)

1536 ÷ 2 = 768 (not a cube)

1536 ÷ 3 = 512 (cube)

So,the volume of the largest cube = 512

The side of the largest cube = ³✓512 = 8 metres

Hence,the largest cube that we can pack in that box has the side of 8 metres.

Answered by Anonymous

Answer:

hope it helps you bro

Step-by-step explanation:

i) For, calculating the total number of smaller cubes that can be packed into the box,we have to calculate the volume of both the bigger box and one smaller cube.