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The diagonal of cube is 16 root 3 cm find its surface area and volume
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The diagonal of cube is 16 root 3 cm find its surface area and volume
Understanding the Cube's Diagonal
The diagonal of a cube can be expressed using the formula:
Diagonal = a * √3, where 'a' is the length of one side of the cube.
Given that the diagonal is 16√3 cm, we can find the side length 'a'.
Calculating the Side Length
- Set the diagonal equal to the formula:
a * √3 = 16√3
- To solve for 'a', divide both sides by √3:
a = 16 cm
Calculating the Surface Area
The surface area (SA) of a cube can be calculated using the formula:
SA = 6 * a²
- Substitute the value of 'a':
SA = 6 * (16)²
SA = 6 * 256
SA = 1536 cm²
Calculating the Volume
The volume (V) of a cube is determined using the formula:
V = a³
- Substitute the value of 'a':
V = (16)³
V = 4096 cm³
Summary of Results
- Side Length: 16 cm
- Surface Area: 1536 cm²
- Volume: 4096 cm³
This comprehensive approach allows you to understand how to derive the surface area and volume of a cube when the diagonal is known.
The diagonal of a cube can be expressed using the formula:
Diagonal = a * √3, where 'a' is the length of one side of the cube.
Given that the diagonal is 16√3 cm, we can find the side length 'a'.
Calculating the Side Length
- Set the diagonal equal to the formula:
a * √3 = 16√3
- To solve for 'a', divide both sides by √3:
a = 16 cm
Calculating the Surface Area
The surface area (SA) of a cube can be calculated using the formula:
SA = 6 * a²
- Substitute the value of 'a':
SA = 6 * (16)²
SA = 6 * 256
SA = 1536 cm²
Calculating the Volume
The volume (V) of a cube is determined using the formula:
V = a³
- Substitute the value of 'a':
V = (16)³
V = 4096 cm³
Summary of Results
- Side Length: 16 cm
- Surface Area: 1536 cm²
- Volume: 4096 cm³
This comprehensive approach allows you to understand how to derive the surface area and volume of a cube when the diagonal is known.
Community Answer
The diagonal of cube is 16 root 3 cm find its surface area and volume
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The diagonal of cube is 16 root 3 cm find its surface area and volume
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The diagonal of cube is 16 root 3 cm find its surface area and volume 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 The diagonal of cube is 16 root 3 cm find its surface area and volume covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diagonal of cube is 16 root 3 cm find its surface area and volume.
The diagonal of cube is 16 root 3 cm find its surface area and volume 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 The diagonal of cube is 16 root 3 cm find its surface area and volume covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The diagonal of cube is 16 root 3 cm find its surface area and volume.
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