Question

Find the value of (circumference of Q + circumference of R) / circumference of P ?​

Answer 1

QUESTION:

The circles PQR are all tangent to each other. Their centres all lie on the diameter of P as shown in the figure. what is the value of (Circumference of Q + Circumference of R ) ÷ Circumference of P

ANSWER:

(Circumference of Q + Circumference of R ) ÷ Circumference of P = 1

GIVEN:

• The circles PQR are all tangent to each other.

• Their centres all lie on the diameter of P.

TO FIND:

• The value of (Circumference of Q + Circumference of R ) ÷ Circumference of P

EXPLANATION:

Let radius of circle Q = r and radius of circe R = r'

Diameter of the circle P contains all the three circles' diameters.

Diameter of circle P = r + r + r' + r'

Diameter of circle P = 2r + 2r'

Diameter of circle P = 2(r + r')

Radius of the circle = diameter / 2

Radius of circle P = 2(r + r') / 2

Radius of circle P = (r + r')

Circumference of circle = 2πR

[where R is the radius of the circle]

Let Circumference of Q = c

c = 2πr

Let Circumference of R = c'

c' = 2πr'

Let Circumference of P = C

C = 2π(r + r')

On Substituting these values, we will get

$\dfrac{2\pi r + 2\pi r'}{2\pi(r + r') }$

Take 2π as common.

$\dfrac{2\pi(r + r')}{2\pi(r + r') }$

Cancel 2π on both numerator and denominator.

$\dfrac{(r + r')}{(r + r') } = 1$

Hence the value of (Circumference of Q + Circumference of R ) ÷ Circumference of P = 1

Answer 2

Answer:

2 cm

Step-by-step explanation: