Question

9. The circumference of a circle exceeds its diameter by 180 cm. Calculate (i) the radius (ii) the circumference and (iii) the area of the circle.

[Hint. (20 - 2r) = 180.)​

Answer 1

Answer: i) the radius: 42cm (ii) the circumference: 264 cm and (iii) the area of the circle: 5,539 cm².

Step by step explanation:

• Given: Circumference of the circle exceeds it's diameter by 180 cm.

• To find: (i) the radius (ii) the circumference and (iii) the area of the circle.

Lets assume the radius as 'r' cm.

Thus, it's diameter = d = 2r.

Now, We know that,

• Circumference of circle = 2πr

Thus, As given:

2πr - 2r = 180 cm

2r(π - 1) = 180

2r(3.14 - 1) = 180

6.28r - 2r = 180

4.28r = 180

r = 180/4.28

r = 42 cm

Thus, we got the value of I) radius i.e: 42 cm.

Now,

• ii) Circumference = 2 π r

= 2 × 3.14 × 42

= 264 cm (approx.)

• iii) Area of circle = πr²

= 3.14 × 42 × 42

= 5,539 cm² (approx.)

Thus, we got all the answers.

Final answer:

Radius of the circle is 42 cm, Circumference: 264 cm and Area: 5,539 cm² (approx.)

Answer 2

AnswEr:

• Radius of circle is 42 cm.

• Circumference of circle is 264 cm.

• Area of circle is 5544 cm²

ExplanaTion:

It is given that, circumference exceeds its diameter by 180 cm.

$\therefore$ $\large{\boxed{\sf{\red{(2 \pi r - 2r) = 180}}}}$

Taking 2r as common,

: $\implies$ $\sf{2r( \pi - 1 )= 180}$

Substitute π = $\sf{\bold{\dfrac{22}{7}}}$

: $\implies$ $\sf{( \dfrac{22}{7} - 1) 2r = 180}$

: $\implies$ $\sf{(\dfrac{22}{7} - 1) 2r = 180}$

Taking LCM,

: $\implies$ $\sf{r = \dfrac{180 \times 7}{15 \times 2}}$

: $\implies$ $\sf{\blue{r = 42\:cm}}$

Hence, radius of circle is 42 cm.

$\rule{200}2$

Now, we have to find circumference and area of circle.

We know that,

★ $\large{\boxed{\sf{\pink{Circumference\:of\:circle\:=\:2 \pi r}}}}$

Substituting the values,

: $\implies$ $\sf{Circumference\:of\:circle\:=\:2 \: \times \dfrac{22}{7 \! \! \! \backslash} \times \: 42 \! \! \! \! \! \! \: \backslash}$

: $\implies$ $\sf{\green{Circumference\:of\:circle\:=\:264\:cm}}$

Hence, circumference of circle is 264 cm.

We also know that,

★ $\large{\boxed{\sf{\purple{Area\:of\:circle\:=\: \pi r^2}}}}$

: $\implies$ $\sf{Area\:of\:circle\:=\: \dfrac{22}{7 \! \! \! \backslash} \times {42 \!\!\!\! \backslash} \: \: \times 42}$

: $\implies$ $\sf{\red{Area\:of\:circle\:=\:5544\:cm^2}}$

Hence, area of circle is 5544 cm²