Question

The radius of a sphere is measured as (2.1 ± 0.5) cm. Calculate its surface area with error limits.

Answer 1

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Answer 2

Answer:

The surface area with error limits is (55.4±26.4)cm².

Explanation:

The surface area of the sphere is calculated as,

$S=4\pi r^2$     (1)

Where,

S=surface area of the sphere

r=radius of the sphere

From the question we have,

Radius=(2.1±0.5)cm

Now by putting the value of "2.1" in equation (1) we get;

$S=4\pi\times (2.1)^2$

$S=55.4cm^2$    (2)

Now,

$\frac{\Delta A}{A} =2\times \frac{\Delta r}{r}$       (3)

By placing all the values in equation (3) we get;

$\frac{\Delta A}{55.4} =2\times \frac{0.5}{2.1}$

$\Delta A=2\times \frac{0.5}{2.1}\times 55.4$

$\Delta A=26.4cm^2$     (4)

Hence, the surface area with error limits is (55.4±26.4)cm².

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