The edge of three of the four cubes are 1cm, 9cm & 10cm respectively. If total volume of two cubes with 9cm &10 cm edge is equal to the remaining two cubes, find the edge of the remaining fourth cube
Answers
Step-by-step explanation:
Given :-
The edge of three of the four cubes are 1cm, 9cm & 10cm respectively.
The total volume of two cubes with 9cm & 10 cm edge is equal to the remaining two cubes.
To find :-
The edge of the remaining fourth cube
Solution :-
Given that
The edge of the first cube = 1 cm
The edge of the second cube = 9 cm
The edge of the third cube = 10 cm
Let the edge of the fourth cube be X cm
We know that
Volume of a cube is a³ cubic.units
where, a is the edge of the cube
Now,
Volume of the first cube
= 1³ cm³
= 1 ×1 ×1 cm³
= 1 cm³
Volume of the first cube = 1 cm³
Volume of the second cube
= 9³ cm³
= 9×9×9 cm³
= 729 cm³
Volume of the second cube = 729 cm³
Volume of the third cube
= 10³ cm³
= 10×10×10 cm³
= 1000 cm³
Volume of the third cube = 1000 cm³
Volume of the fourth cube
= X³ cm³
Volume of the fourth cube = X³ cm³
Given that
Total Volumes of two cubes with 9 cm and 10 cm
= Total Volume of two cube with 1 cm
and X cm
=> 729 + 1000 = 1 + X³
=> 1729 = 1+X³
=> 1729-1 = X³
=> 1728 = X³
=> X³ = 1729
=> X³ = 12×12×12
=> X³ = 12³
=> X = 12 cm
Therefore, The edge of the fourth cube
= 12 cm
Answer :-
The edge of the fourth cube is 12 cm
Used formulae:-
→ Volume of a cube is a³ cubic.units
Where, a is the edge of the cube
Given :-
The edge of three of the four cubes are 1cm, 9cm & 10cm respectively.
If total volume of two cubes with 9cm &10 cm edge is equal to the remaining two cubes.
To Find :-
The edge of the remaining fourth cube.
Solution :-
Let the edge of 4th cube be x cm .
Volume of 1st cube = a³
= 1³
= 1 cm³
Volume of 2nd cube = a³
= 9³
= 729 cm³
Volume of 3rd cube = a³
= 10³
= 1000 cm³
Volume of 4th cube = a³
= x³
then, according to the question .
⇒ 729 + 1000 = 1 + x³
⇒ x³ = 1729 - 1
⇒ x = 12cm
∴ Edge of 4th cube is 12cm .