Question

if the area of a ring is 1570 cm square and the outer radius of the ring is 30 cm then the width of the ring is (where π=3.14​

Answer 1

Answer:

Let us given R=1570cm & r=30cm

Area of outer circle =π(30)^2

                                 =22/7 ×900=2816

Area of inner circle =π(1570)2

                                 =22/7 × 2,464,900=7,746,816

∴ area of the ring=22/6(2464900−7746816)

                              =22/7(5,281,916)

                              =16,600,307

Step-by-step explanation:

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Answer 2

Answer:

Hence, the width of the ring is $10cm$.

Step-by-step explanation:

Concept:

The area of a ring can be estimated by deducting the area of the smaller circle from the area of the bigger circle as a ring is a shape consisting of two concentric circles.

Given:

The area of a ring $= 1570$ cm square

The outer radius of the ring $= 30$ cm

To find:

We have to find the width of the ring.

Solution:

Apply the formula given below:

$&\mathrm{A}=\pi R^{2}-\pi r^{2} \\A&=\pi \times\left(R^{2}-r^{2}\right)$

In this formula, $R$ is the outer radius and $r$ is the inner radius.

Since Area $A$ $=1570 \mathrm{~cm}^{2}$ and $R=30 \mathrm{~cm}$

$&1570=\pi \times\left(30^{2}-r^{2}\right)$

$&1570=3.14 \times\left(30^{2}-r^{2}\right) \\&30^{2}-r^{2}=\frac{1570}{3.14} \\&30^{2}-r^{2}=500$

$&r^{2}=500-900 \\&r^{2}=400 \\&r=20 \mathrm{~cm}$

Thus, the inner radius is $20 \mathrm{~cm}$.

Now, We know that the width of the ring is the variance between the outer radius and inner radius. So,

Width $= R - r$

       $= 30cm - 20cm\\= 10cm$

Therefore, the width of ring is $10cm$.

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