Question
Download Solution PDFIf the radius of a sphere is increased by 125%, then by what percentage will its surface area increase (correct to two decimal places)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Initial radius of the sphere = r
Increased radius of the sphere = r + 125% of r
Increased radius of the sphere = r + 1.25r = 2.25r
Formula Used:
Surface area of a sphere = 4πr2
Calculation:
Initial surface area = 4πr2
New surface area with increased radius = 4π(2.25r)2
⇒ New surface area = 4π(5.0625r2)
⇒ New surface area = 20.25πr2
Increase in surface area = New surface area - Initial surface area
⇒ Increase in surface area = 20.25πr2 - 4πr2
⇒ Increase in surface area = 16.25πr2
Percentage increase in surface area = (Increase in surface area / Initial surface area) × 100
⇒ Percentage increase in surface area = (16.25πr2 / 4πr2) × 100
⇒ Percentage increase in surface area = (16.25 / 4) × 100
⇒ Percentage increase in surface area = 4.0625 × 100
⇒ Percentage increase in surface area = 406.25%
The percentage increase in surface area is 406.25%.
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