Question

Find the number of circles with radius 1m are needed for the sum of their areas to equal the area of a circle with radius 3m.(a) 3. (b) 6. (c) 9. (d) 27​

Answer 1

Answer:

Option ( C ) is correct.

Step-by-step explanation:

Let the number of circles with radius 1 m be n.

Here,

Sum areas of n circles of radius 1 m is equal to the area of a circle with radius 3 m.

Therefore,

= > Sum of areas of n circles with radius 1 m = area of circle with radius 3 m

= > n x area of one circle with radius 1 m = area of circle with radius 3 m

= > n x { π( 1 m )^2 } = π( 3 m )^2 { Area of circle = πr^2, where r is radius }

= > n x π x 1 m^2 = π x 9 m^2

= > n = 9

Hence the required number of circles with radius 1 m is 9.

Option ( C ) is correct.

Answer 2

Step-by-step explanation:

$\huge\red{ANSWER :-}$

EXPLAINATION :-

Let the number of circles with radius 1m be n.

» Sum areas of n circles of radius 1m is equal to the area of a circle with radius 3m.

» Therefore,

sum of areas of n circle with radius 1 m = area of circle with radius 3m.

» n× area of circles with radius 1m

= area of circle with radius 3m.

» n ×{ π(1m)²}= π (3m)²

» AREA OF CIRCLE IS πr²

» n×π×1m² = π 9m²

» n = 9

$\huge\boxed{ANSWER \:\:IS\:\: OPTION\:\: C\:\: (9)}$