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If the radius of a sphere is increased by 50% then find the increase in surface area of the sphere.?
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If the radius of a sphere is increased by 50% then find the increase i...
Understanding the Problem
When the radius of a sphere is increased by 50%, we can analyze how this affects the surface area.
Initial Radius and Increased Radius
- Let the original radius be r.
- With a 50% increase, the new radius becomes:
- New Radius = r + (50/100) * r = 1.5r.
Surface Area Formula
The formula for the surface area (SA) of a sphere is given by:
- SA = 4 * π * r^2.
Calculating Initial Surface Area
- Initial Surface Area (SA_initial) = 4 * π * r^2.
Calculating New Surface Area
- New Surface Area (SA_new) = 4 * π * (1.5r)^2.
- Simplifying this:
- SA_new = 4 * π * (2.25r^2) = 9 * π * r^2.
Finding the Increase in Surface Area
- Increase in Surface Area = SA_new - SA_initial.
- This gives us:
- Increase = (9 * π * r^2) - (4 * π * r^2) = (5 * π * r^2).
Percentage Increase in Surface Area
- To find the percentage increase:
- Percentage Increase = (Increase / SA_initial) * 100
- Percentage Increase = [(5 * π * r^2) / (4 * π * r^2)] * 100 = 125%.
Conclusion
When the radius of a sphere is increased by 50%, the surface area increases by 125%. This shows a significant expansion in the surface area due to the increase in radius.
When the radius of a sphere is increased by 50%, we can analyze how this affects the surface area.
Initial Radius and Increased Radius
- Let the original radius be r.
- With a 50% increase, the new radius becomes:
- New Radius = r + (50/100) * r = 1.5r.
Surface Area Formula
The formula for the surface area (SA) of a sphere is given by:
- SA = 4 * π * r^2.
Calculating Initial Surface Area
- Initial Surface Area (SA_initial) = 4 * π * r^2.
Calculating New Surface Area
- New Surface Area (SA_new) = 4 * π * (1.5r)^2.
- Simplifying this:
- SA_new = 4 * π * (2.25r^2) = 9 * π * r^2.
Finding the Increase in Surface Area
- Increase in Surface Area = SA_new - SA_initial.
- This gives us:
- Increase = (9 * π * r^2) - (4 * π * r^2) = (5 * π * r^2).
Percentage Increase in Surface Area
- To find the percentage increase:
- Percentage Increase = (Increase / SA_initial) * 100
- Percentage Increase = [(5 * π * r^2) / (4 * π * r^2)] * 100 = 125%.
Conclusion
When the radius of a sphere is increased by 50%, the surface area increases by 125%. This shows a significant expansion in the surface area due to the increase in radius.
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If the radius of a sphere is increased by 50% then find the increase in surface area of the sphere.?
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If the radius of a sphere is increased by 50% then find the increase in surface area of the sphere.? 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 If the radius of a sphere is increased by 50% then find the increase in surface area of the sphere.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the radius of a sphere is increased by 50% then find the increase in surface area of the sphere.?.
If the radius of a sphere is increased by 50% then find the increase in surface area of the sphere.? 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 If the radius of a sphere is increased by 50% then find the increase in surface area of the sphere.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the radius of a sphere is increased by 50% then find the increase in surface area of the sphere.?.
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