Question

Ram came to know that raw cheese is very healthy for our health so he brought a large piece
of cheese to his home which is cubical in shape and its volume is 729 cm. His family has total
27 members in it. So he wants to cut the cheese with a knife and distribute it among his family
members.
(1) What are the minimum number of single straight cuts required to divide the given
cuboidal cheese into 27 equal parts?
(2) What is the surface area of each small cubical cheese? 5h​

Answer 1

1) Minimum cuts require are 10.

2) Surface area of each small cubicle cheese is 78 cm.

Step-by-step explanation:

Since it is cubical of volume 729 cm^3

so, each side will be

a=∛729

Which is equal to 9 cm.

Which means each side of cube is 9 cm.

Now cutting from one side of the cube in 9 equal parts

As depicted in the figure 1 with cuts number 1 ,2 ,3...8.

So by applying 8cuts it will be divided into 9equal parts.

Now, cutting horizontally into 3 equal parts with cut number 9 ,10.

It divides the cheese into 27 equal parts, which is also numbered in the figure.

Hence, 10 cuts are required to divide it into 27 equal parts.

2).

dimensions of each part is 1 cm , 3 cm ,9 cm

hence surface area of each small part is

2(1 X 3) + 2(1 X 9) + 2(9 X 3) = 78 cm^2

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