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if the radius of a sphere is measured as 'p'cm with an error 0.03cm, then find the approximate error in calculating its volume

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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.