The radius of a sphere is measured as 9cm with an error of 0.03 cm , find the approximate error in its surface area.
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Secondary SchoolMath 5+3 pts
If the radius of a sphere is measured as 9 cm with an error of 0.03 cm,then find the approximate error in calculating its surface area
Report by Shubham4444comp9jhv1 30.05.2018
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tiwaavi
Tiwaavi ★ Brainly Teacher ★
Given conditions ⇒
Radius of the sphere(r) = 9 cm.
Error in the Measurement of the radius(Δr) = 0.03 cm.
Now, We know, the Formula,
Surface Area of the sphere(A) = 4πr²
∴ A = 4πr²
Now, Differentiating both sides of the Equation,
dA/dr = 8πr
Now,
ΔA = A × Δr
⇒ ΔA = dA/dr × (0.03)
⇒ ΔA = 8πr × 0.03
⇒ ΔA = 8 × 22/7 × 9 × 0.03
⇒ ΔA = 47.52/7
∴ ΔA = 6.78 (or 2.16π) cm²
Hence, the Approximate Errors in the Measurement of the surface area will be 6.18 cm².