Cube a has edges of 4 Cm
Cube b has edges of length 30% less than that of cube A
Express the difference in the volumes of the two cubes as percentage of the volume of cube A
Answers
Step-by-step explanation:
Given :-
Cube a has edges of 4 Cm.Cube b has edges of length 30% less than that of cube A.
To find :-
Express the difference in the volumes of the two cubes as percentage of the volume of cube A?
Solution :-
The edge of a cube A = 4 cm
We know that
Volume of a cube whose edge a units is a³ cubic units
Volume of the given cube A
=>V = 4³ Cm³
=> V = 4×4×4 Cm³
=> V = 64 Cm³
Volume of the cube A = 64 Cm³
Edge of the cube B
=> 30% less than the edge of A
=> 4 - 30% of 4 cm
=> 4-(30% ×4)
=> 4-(30×4/100)
=> 4-(120/100)
=> 4-(6/5)
=> (20-6)/5
=> 14/5 cm
=> 2.8 cm
Edge of the cube B = 2.8 cm
Volume of the cube B = (2.8)³ Cm³
=> 2.8×2.8×2.8 Cm³
=> 21.952 Cm³
Volume of the cube B = 21.952 cm³
Difference between the volumes of the two cubes
=> 64 - 21.952
=> 42.048 Cm³
Difference between the volumes = 42.048 Cm³
The Percentage of the difference of the volumes of the two cubes of the Volume of A
=> (Difference/Volume of A)×100
=> [(42.048/64)×100]%
=> [(42.048×100)/64]%
=> (4204.8/64)%
=> 65.7%
Required Percentage = 65.7%
Answer:-
65.7% of the volume of cube A is the difference in the volumes of the two cubes.
Used formulae:-
→ Volume of a cube whose edge a units is a³ cubic units