Question

A cuboidal box is a three-dimensional figure, with varying length. breadth, and height whereas in a cubical box; length, breadth, and height are all equal to each other.

The space enclosed by a three-dimensional figure is known as it is volume. Volume of a cuboid having length 1, breadth b and height h is (1 xbxh) unit”.

Volume of a cube having side l is (X 1 x 1) unit

It is Jatin's birthday today!

He has 100 cube-shaped chocolates of side 2cm.

As a return gift for his friends. Jatin wants to pack the least number of chocolates in a box, each box containing same number of chocolates. He must make boxes for this purpose, keeping in mind that he has 12 friends.

Jatin takes four colourful paper sheet, cach measuring 12cm x 12cm.

His task is to make four cuboidal or cubical boxes (without lid) of different volumes. by folding and then decide as to which dimensions should he choose for making the gift boxes. Let us build a box from Jatin's 12em x 12em square sheet. You can do this by cutting out congruent squares at all the corners of the sheet.

Let us begin by drawing lem x lcm squares on each corner of the sheet.

Next, cut out all four squares from the corners. Fold up the sides along the dotted lines (as shown in the figure) and paste them together.Question 1:- What are the dimensions of the base of box 1?

a) 10cm x 10cm

b) 10cm x 1cm

c) 10cm x 2cm

d) 12cm x 10cm

Now take another rectangular sheet of same size and cut 2cm x 2cm squares out of each corner and make another box by folding up the sides.​

Answer 1

the answer is 100,10,20,120

Answer 2

Given :  Sheet 12 x 12 cm

To Find : Cut corner Square to find dimension of open cuboid

dimensions of the base of box 1  when  1cm square box are cut.

Solution:

if x cm corner squares are cut

Then Length , breadth  = 12 - 2x

Height =  x  cm

x = 1

=> Dimensions are  10 x 10 x 1  

Dimension of Base = 10 x 10

Volume = 100

x = 2

=> Dimensions are  8 x 8 x 2

Dimension of Base = 8 x 8  

Volume = 128

x = 3

=> Dimensions are  6 x 6 x 3

Dimension of Base = 4 x 4  

Volume = 108

x = 4

=> Dimensions are  4 x 4 x 4

Dimension of Base = 4 x 4

Volume = 64

x = 5

=> Dimensions are  2 x 2 x 5

Dimension of Base = 2 x 2

Volume = 20

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