Question

if the area of the ring is 1570m2 and outer radius is 30 cm then width of ring is

Answer 1

Answer:

If the area of the ring is 1570cm² and outer radius is 30 cm then width of ring is 10cm.

Step-by-step explanation:

The area of the ring is given as 1570cm² and the radius of the outer circle of the ring is given as 30cm.

Since a ring is a shape made of two concentric circles of the area of a ring can be calculated using by subtracting the area of the smaller circle from the area of the larger circle. That is

A = $\pi R^{2} -\pi r^{2}$

= $\pi \times {(R^{2} -r^{2} )}$

where R is the outer radius and r is the inner radius.

Since Area = 1570cm² and R = 30cm,

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

$1570 = 3.14 \times {(30^{2} -r^{2} )}$

$30^{2} -r^{2} =\frac{1570}{3.14}$

$30^{2} -r^{2} =500$

$r^{2} =500-900$

$r^{2} =400$

$r=20cm$

That is, the inner radius is 20cm.

Now, the width of the ring is the difference between the outer radius and inner radius. That is,

Width = R - r

         = 30cm - 20cm

         = 10cm.

Hence if the area of the ring is 1570cm² and outer radius is 30cm then width of ring is 10cm.

Answer 2

Answer:

If the area of the ring is 1570cm² and outer radius is 30 cm then width of ring is 10cm.

Step-by-step explanation:

The area of the ring is given as 1570cm² and the radius of the outer circle of the ring is given as 30cm.

Since a ring is a shape made of two concentric circles of the area of a ring can be calculated using by subtracting the area of the smaller circle from the area of the larger circle. That is

A = \pi R^{2} -\pi r^{2}πR

2

−πr

2

= \pi \times {(R^{2} -r^{2} )}π×(R

2

−r

2

)

where R is the outer radius and r is the inner radius.

Since Area = 1570cm² and R = 30cm,

1570 = \pi \times {(30^{2} -r^{2} )}1570=π×(30

2

−r

2

)

1570 = 3.14 \times {(30^{2} -r^{2} )}1570=3.14×(30

2

−r

2

)

30^{2} -r^{2} =\frac{1570}{3.14}30

2

−r

2

=

3.14

1570

30^{2} -r^{2} =50030

2

−r

2

=500

r^{2} =500-900r

2

=500−900

r^{2} =400r

2

=400

r=20cmr=20cm

That is, the inner radius is 20cm.

Now, the width of the ring is the difference between the outer radius and inner radius. That is,

Width = R - r

= 30cm - 20cm

= 10cm.

Hence if the area of the ring is 1570cm² and outer radius is 30cm then width of ring is 10cm