The diameter of a sphere is increased by 25% by ehat percent its c.s.a. is increased?
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Answered by
1
let diameter=2r
∴radius=r
∴c.s.a=4πr²
now,
diameter=2r+(25/100×2r)=2r+r/2=5r/2
∴radius=5r/4
∴c.s.a=4π×5r/4×5r/4=25πr²/4
∴increase=25πr²/4 - 4πr²= 9πr²/4
∴increase %=9πr²/4÷4πr² ×100
∴radius=r
∴c.s.a=4πr²
now,
diameter=2r+(25/100×2r)=2r+r/2=5r/2
∴radius=5r/4
∴c.s.a=4π×5r/4×5r/4=25πr²/4
∴increase=25πr²/4 - 4πr²= 9πr²/4
∴increase %=9πr²/4÷4πr² ×100
Answered by
1
the percent decrease in surface area of the sphere is 43.75%
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