Question

A cubical wooden block of side 9 cm
has been cut into small cubes of side 3
cm each. The ratio of surface area of
wooden block to the total surface
area of new cubes made is
(1) 3:1
(2) 1:3
(3) 1:2
(4) 2:1​

Answer 1

Answer:

3:1 ratio is the answer to this question.....

Answer 2

The ratio of surface area of wooden block to the total surface area of new cubes made is 1:3 (Option 2).

Given data :

Length of one side of the bigger cube is 9 centimetres.

Length of one side of the smaller cube is 3 centimetres.

• At first we have to calculate the volumeof the bigger cube by using the following mathematical formula :

= (Side)³

= (9)³

= 729 cm³

• Then we have to calculate the volume of the smaller cube by using the following mathematical formula :

= (side)³

= (3)³

= 27 cm³

• Now,we have to calculate the number of smaller cubes by using the following mathematical formula :

= Volume of bigger cube / Volume of smaller cube

= 729/29

= 27

• Now,we have to calculate the surface area of the bigger cube

= 6 × (side)² [a cube has 6 surfaces]

= 6×(9)²

= 6×81

= 486 cm²

• The surface area of the smaller cube

= 6×(side)²

= 6×(3)²

= 6×9

= 54 cm²

• Total surface area of the smaller cubes = 54×27 = 1458 cm²

So,the ratio of the surface area bigger cube to the total surface area of the smaller cubes = 486:1458 = 1:3 (answer)