Question

The area of two concentric circles are 1386 $cm^{2}$ and 962.5$cm^{2}$. The width of the ring is:
a) 4.2 cm
b) 3.8 cm
c) 3.5 cm
d) 2.8 cm

Question Credit: NTSE Question Paper 2017-18

Answer 1

Answer:

c) 3.5 cm

Step-by-step explanation:

πR^2=1386 So R=21cm πr^2=962.5 So r=17.5cm Thus width of ring = 21-17.5=3.5cm

Answer 2

Answer :-

Option c) 3.5 cm

_______________________

Given:-

Area of two circles is 1386 cm² and 962.5 cm².

Find:-

• Width of the ring.

Means, the larger radius of circle - smaller radius of the circle.

Solution:-

Let (R) be the radius of a circle whose area is 1386 cm² and (r) be the radius of circle 962.5 cm².

So, here -

• The larger circle is of area 1386 cm²
• The smaller circle is of area 962.5 cm²

Now,

→ Area of circle = πr²

$\sf{For\:larger\:circle}$

= 1386 = πr²

= 1386 = 22/7 × R²

= 1386 × 7 = 22R²

= 9702/22 = R²

= 441 = R²

= √441 = R

= 21 = R

$\implies$ R = 21 cm

$\sf{For\:smaller\:circle}$

= 962.5 = πr²

= 962.5 = 22/7 × r²

= 962.5 × 7 = 22r²

= 6737.5/22 = r²

= 306.25 = r²

= √306.25 = r

= 17.5 = r

$\implies$ r = 17.5 cm

•°• Width of the ring = R - r

= 21 - 17.5

$\implies$ 3.5 cm