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It takes 2 liters to paint the surface of a solid sphere. If this solid sphere is sliced into 4 identical
pieces, how many liters will be required to paint all the surfaces of these 4 pieces. ?
pieces, how many liters will be required to paint all the surfaces of these 4 pieces. ?
Verified Answer
It takes 2 liters to paint the surface of a solid sphere. If this soli...
If you slice a solid sphere into 4 identical pieces, you will get 4 solid hemispheres. Each of these hemispheres has a surface area that is half the surface area of the original sphere. Since it takes 2 liters to paint the surface of the original sphere, it will take 2/2=1 liter to paint the surface of each of the 4 hemispheres. Therefore, it will take a total of 4 liters of paint to paint the surface of all 4 pieces.
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It takes 2 liters to paint the surface of a solid sphere. If this soli...
Given:
- The surface area of a solid sphere requires 2 liters of paint.
To Find:
- The amount of paint required to paint all the surfaces of 4 identical pieces obtained by slicing the sphere.
Solution:
Step 1: Calculate the surface area of the original sphere:
- The surface area of a sphere can be calculated using the formula: A = 4πr², where A is the surface area and r is the radius.
- Since the given information only provides the amount of paint required, we need to find the radius of the sphere first.
- Let's assume the radius of the sphere is 'R'.
- So, the surface area of the original sphere is: A₁ = 4πR².
Step 2: Calculate the surface area of each piece:
- When the solid sphere is sliced into 4 identical pieces, each piece will have the same surface area.
- Therefore, the surface area of each piece is: A₂ = A₁/4.
Step 3: Calculate the amount of paint required for each piece:
- Since the given information states that 2 liters of paint are required to paint the surface area of the original sphere, we can assume that the same amount of paint is required for each piece.
- Therefore, the amount of paint required for each piece is: P = 2 liters.
Step 4: Calculate the total amount of paint required for all 4 pieces:
- Since each piece requires 2 liters of paint, the total amount of paint required for all 4 pieces is: Total Paint = 4P = 4 * 2 = 8 liters.
Conclusion:
- In order to paint all the surfaces of the 4 identical pieces obtained by slicing the original sphere, 8 liters of paint will be required.
- The surface area of a solid sphere requires 2 liters of paint.
To Find:
- The amount of paint required to paint all the surfaces of 4 identical pieces obtained by slicing the sphere.
Solution:
Step 1: Calculate the surface area of the original sphere:
- The surface area of a sphere can be calculated using the formula: A = 4πr², where A is the surface area and r is the radius.
- Since the given information only provides the amount of paint required, we need to find the radius of the sphere first.
- Let's assume the radius of the sphere is 'R'.
- So, the surface area of the original sphere is: A₁ = 4πR².
Step 2: Calculate the surface area of each piece:
- When the solid sphere is sliced into 4 identical pieces, each piece will have the same surface area.
- Therefore, the surface area of each piece is: A₂ = A₁/4.
Step 3: Calculate the amount of paint required for each piece:
- Since the given information states that 2 liters of paint are required to paint the surface area of the original sphere, we can assume that the same amount of paint is required for each piece.
- Therefore, the amount of paint required for each piece is: P = 2 liters.
Step 4: Calculate the total amount of paint required for all 4 pieces:
- Since each piece requires 2 liters of paint, the total amount of paint required for all 4 pieces is: Total Paint = 4P = 4 * 2 = 8 liters.
Conclusion:
- In order to paint all the surfaces of the 4 identical pieces obtained by slicing the original sphere, 8 liters of paint will be required.
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It takes 2 liters to paint the surface of a solid sphere. If this solid sphere is sliced into 4 identical pieces, how many liters will be required to paint all the surfaces of these 4 pieces. ?
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It takes 2 liters to paint the surface of a solid sphere. If this solid sphere is sliced into 4 identical pieces, how many liters will be required to paint all the surfaces of these 4 pieces. ? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about It takes 2 liters to paint the surface of a solid sphere. If this solid sphere is sliced into 4 identical pieces, how many liters will be required to paint all the surfaces of these 4 pieces. ? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It takes 2 liters to paint the surface of a solid sphere. If this solid sphere is sliced into 4 identical pieces, how many liters will be required to paint all the surfaces of these 4 pieces. ?.
It takes 2 liters to paint the surface of a solid sphere. If this solid sphere is sliced into 4 identical pieces, how many liters will be required to paint all the surfaces of these 4 pieces. ? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about It takes 2 liters to paint the surface of a solid sphere. If this solid sphere is sliced into 4 identical pieces, how many liters will be required to paint all the surfaces of these 4 pieces. ? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It takes 2 liters to paint the surface of a solid sphere. If this solid sphere is sliced into 4 identical pieces, how many liters will be required to paint all the surfaces of these 4 pieces. ?.
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