Find the surface area of a cube whose volume is 3375 cm³. Also find its diagonals.
Answers
Given :-
The volume of a cube is 3375 cm³
To find :-
i) The surface area of the cube .
ii) The length of the cube.
Solution :-
Given that
The volume of a cube = 3375 cm³
We know that
Volume of a cube whose length of its edge is a units is a³ cubic units
Therefore, a³ = 3375
=> a³ = 15³
=> a = 15
The length of the edge of the cube = 15 cm
We know that
Total Surface Area of a cube is 6a² sq.units
Total Surface Area of the cube = 6×15² cm²
=> TSA = 6×225 cm²
=> TSA = 1350 cm²
We know that
The length of the diagonal of a cube is √3 a units
The length of the diagonal of the given cube
= √3 × 15 cm
= 15√3 cm or
= 15×1.732 cm
= 25.98 cm
Answer :-
→ Total Surface Area of the cube
= 1350 cm²
→ The length of the diagonal of the cube
= 15√3 cm or 25.98 cm
Used formulae:-
→ Total Surface Area of a cube is 6a² sq.units
→ Volume of a cube whose length of its edge is a units is a³ cubic units
→ The length of the diagonal of a cube is √3 a units
Given :
Volume of cube = 3375cm³
Volume of a cube whose length of its edge a is a³ cubic units.
Length of diagonal of a cube is √2 a units.
Approximate value:
_____________________________________
Additional information -