If the ratio of the volumes of two cubes is 1 : 8, then find the ratio of the total surface areas of the two cubes.
Answers
Answer:
1:4
Step-by-step explanation:
Volume = a³
Side of 1st cube = Cube root 1 = 1
Side of 2nd cube = Cube root 8 = 2
Therefore sides are in the ratio 1:2
Surface area = 6a²
Surface area of 1st cube = 6×1 = 6
Surface area of 2nd cube = 6×4 = 24
Hence ratio is 6:24 which is equal to 1:4
Step-by-step explanation:
Given :-
The ratio of the volumes of two cubes = 1 : 8
To find :-
Find the ratio of the total surface areas of the two cubes.?
Solution :-
Given that
The ratio of the volumes of two cubes = 1 : 8
We know that
Volume of a cube whose edge is a units is a³ cubic units
Let the edge of the first cube be a units
Then it's volume(V1) = a³ cubic units
Let the edge of the second cube be b units
Then it's volume (V2)= b³ cubic units
Thier ratio = V1 : V2 = a³:b³
According to the given problem
=> a³:b³ = 1:8
=> a³ : b³ = 1³ : 2³
=> a³/b³ = 1³/2³
=> (a/b)³ = (1/2)³
=> a/b = 1/2
=> a : b = 1 : 2
So,
The edge of the first cube = X units
The edge of the second cube = 2X units
We know that
Total Surface Area of a cube = 6a² sq.units
Total Surface Area of the first cube
S1 = 6a² sq.units
Total Surface Areas of the second cube
S2 = 6b² sq.units
Their ratio S1:S2 = 6a²:6b²
=> 6a²/6b²
=> a²/b²
On Substituting the values of a and b then
=> (X)²/(2X)²
=>X²/4X²
=> 1/4
=> 1:4
Therefore, S1:S2 = 1:4
Answer:-
The ratio of the Total Surface Areas of the two cubes is 1:4
Used formulae:-
- Total Surface Area of a cube = 6a² sq.units
- Volume of a cube whose edge is a units is a³ cubic units
Points to know:-
- A cube is a solid which has all the measurements are equal.
- The edge of a cube is a units then
- Lateral Surface Area = 4a² sq.units