Let's assume the original radius of the sphere is r.
The surface area of a sphere is given by the formula 4πr².
The volume of a sphere is given by the formula (4/3)πr³.
If the radius decreases by 0.1%, the new radius would be (r - 0.1/100 * r) = (r - 0.001r) = 0.999r.
1. Percentage Decrease in Surface Area:
New surface area = 4π(0.999r)² = 3.996πr²
% decrease in surface area = ((4πr² - 3.996πr²)/ (4πr²)) × 100%
= ((0.004πr²)/ (4πr²)) × 100%
= 0.1%
Therefore, the surface area of the sphere decreases by 0.1%.
2. Percentage Decrease in Volume:
New volume = (4/3)π(0.999r)³ = 0.999π(4/3)r³ = (0.999)(4/3)πr³
% decrease in volume = ((4/3)πr³ - (0.999)(4/3)πr³)/ ((4/3)πr³) × 100%
= ((4/3)πr³ - (3.996/3)πr³)/ ((4/3)πr³) × 100%
= (0.004/3) × 100%
≈ 0.1333%
Therefore, the volume of the sphere decreases by approximately 0.1333%.
If the radius of a sphere decreases by 0.1%, find the percentage decrease in the surface area and volume
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