Question

The radius of the inner circle and the outer circle as given in the figure is 49m and 56m

respectively. Find the difference of the circumference of both the circles.​

Answer 1

Given

Radius of outer circle (R)= 56m

Radius of inner circle (r)= 49m

To Find :-

we have to find the difference between the circumference of both circle

Solution :-

Difference between their circumference= C. of outer circle - Circumference of inner circle

$\bigstar\tt\ \ Circumference\ of\ circle = 2\pi r \\ \\ \\ :\implies\sf\ Difference \ in\ Circumference= 2\pi R- 2\pi r\\ \\ \\ :\implies\sf\ circumference= 2\pi \big\lgroup R-r\big\rgroup\\ \\ \\ :\implies\sf\ Circumference= 2\times \dfrac{22}{7}\times \big\lgroup 56-49\big\rgroup\\ \\ \\ :\implies\sf\ Circumference= \dfrac{44}{\cancel{7}}\times \cancel{7}\\ \\ \\ \therefore\ \underline{\boxed{\sf\ Difference\ b/w\ their\ circumference= 44m}}$

Some other important formula:-

$\bullet\sf\ Area\ of\ circle= \pi r^2\\ \\ \\ \bullet\sf\ Area\ of\ ring= \pi (R^2-r^2)$

Answer 2

Answer:

Given :-

• The radius of the inner circle and the outer circle is 49 m and 56 m.

To Find :-

• What is the difference between of the circumference of both of the circle.

Formula Used :-

${\red{\boxed{\bold{\large{Circumference\: of\: circle =\: 2{\pi}r}}}}}$

where,

• r = Radius

Solution :-

Given :

• Radius of inner circle (r) = 49 m
• Radius of outer circle (R) = 56 m

We have to find the difference between the circumference. Then, as we know that,

✧ Different between the circumference = Circumference of outer circle - Circumference of inner circle ✧

Then,

According to the question by using the formula we get,

$\sf Difference\: between\: in\: circumference =\: 2{\pi}R -\: 2{\pi}r$

By talking 2π common we get,

$\sf \implies Difference\: between\: in\: circumference =\: 2π\bigg(R - r\bigg)$

$\sf \implies Difference\: between\: in\: circumference\: =\: 2 \times \dfrac{22}{7} \times \bigg(56 - 49\bigg)$

$\sf \implies Difference\: between\: in\: circumference =\: 2 \times \dfrac{22}{\cancel{7}} \times {\cancel{7}}$

$\sf \implies Difference\: between\: in\: circumference =\: 2 \times 22$

$\sf \implies \bold{\purple{Different\: between\: in\: circumference\: =\: 44\: m}}$

$\therefore$ The difference between of the circumference of both the circle is 44 m.

➦ Some Important Formula :-

➠ Area of circle = $\sf\bold{\pink{{\pi}{r}^{2}}}$

➠ Perimeter of semicircle = $\sf\bold{\pink{{\pi}r + 2r}}$

➠ Area of semicircle = $\sf\bold{\pink{\dfrac{{\pi}{r}^{2}}{2}}}$