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2 cubes have volumes in the ratio of 1:27 find the ratio of area of the phase of one to that of other?
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2 cubes have volumes in the ratio of 1:27 find the ratio of area of th...
Understanding Volume Ratio of Cubes
Given that the volumes of two cubes are in the ratio of 1:27, we can derive the side lengths of the cubes from this ratio.
Finding Side Lengths
- The volume of a cube is calculated as V = s³, where s is the length of a side.
- Let the side length of the first cube be s1 and the second cube be s2.
- From the volume ratio:
- V1 : V2 = 1 : 27
- This implies s1³ : s2³ = 1 : 27
- Taking the cube root of both sides gives us:
- s1 : s2 = 1 : 3
Calculating Surface Areas
Now, let’s find the surface areas of the cubes.
- The surface area of a cube is calculated as A = 6s².
- Therefore, the surface areas of the two cubes can be expressed as:
- A1 = 6(s1)²
- A2 = 6(s2)²
Finding the Ratio of Surface Areas
- Since we have established that s1 : s2 = 1 : 3, we can substitute this into the surface area formula:
- A1 : A2 = 6(s1)² : 6(s2)²
- The 6 cancels out, leaving us with:
- (s1)² : (s2)² = (1)² : (3)² = 1 : 9
Final Result
Thus, the ratio of the surface area of one cube to that of the other is 1:9.
Given that the volumes of two cubes are in the ratio of 1:27, we can derive the side lengths of the cubes from this ratio.
Finding Side Lengths
- The volume of a cube is calculated as V = s³, where s is the length of a side.
- Let the side length of the first cube be s1 and the second cube be s2.
- From the volume ratio:
- V1 : V2 = 1 : 27
- This implies s1³ : s2³ = 1 : 27
- Taking the cube root of both sides gives us:
- s1 : s2 = 1 : 3
Calculating Surface Areas
Now, let’s find the surface areas of the cubes.
- The surface area of a cube is calculated as A = 6s².
- Therefore, the surface areas of the two cubes can be expressed as:
- A1 = 6(s1)²
- A2 = 6(s2)²
Finding the Ratio of Surface Areas
- Since we have established that s1 : s2 = 1 : 3, we can substitute this into the surface area formula:
- A1 : A2 = 6(s1)² : 6(s2)²
- The 6 cancels out, leaving us with:
- (s1)² : (s2)² = (1)² : (3)² = 1 : 9
Final Result
Thus, the ratio of the surface area of one cube to that of the other is 1:9.
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2 cubes have volumes in the ratio of 1:27 find the ratio of area of the phase of one to that of other?
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2 cubes have volumes in the ratio of 1:27 find the ratio of area of the phase of one to that of other? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about 2 cubes have volumes in the ratio of 1:27 find the ratio of area of the phase of one to that of other? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2 cubes have volumes in the ratio of 1:27 find the ratio of area of the phase of one to that of other?.
2 cubes have volumes in the ratio of 1:27 find the ratio of area of the phase of one to that of other? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about 2 cubes have volumes in the ratio of 1:27 find the ratio of area of the phase of one to that of other? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 2 cubes have volumes in the ratio of 1:27 find the ratio of area of the phase of one to that of other?.
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