Question

1. If the radius of a circle is 4.2 cm, compute its area and circumference.

2. What is the area of a circle whose circumference is 44 cm?

3. Calculate the area of a sector of angle 60°. Given, the circle is having a radius of 6 cm.​

Answer 1

$\huge{ \underline{\boxed{\red{ \color{red}{\textsf {\textbf{Qu}{\color{blue}{\textbf {\textsf{est}}{\color{green}{\textbf{\textsf{ion}}}{\color{orange}{\textsf{\textbf{~:-}}}}}}}}}}}}}$

1. If the radius of a circle is 4.2 cm, compute its area and circumference.

2. What is the area of a circle whose circumference is 44 cm?

3. Calculate the area of a sector of angle 60°. Given, the circle is having a radius of 6 cm.

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\huge{\boxed{\bullet{\color{orange}{\mathfrak{Answers}}}\bullet}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:$

✯ Answer 1 :-

Radius of circle = 4.2 cm

Area of circle = πr²

✒ $\frac{22}{7}$ × (4.2)²

✒ $\frac{22}{\cancel{7}}$ × ${\cancel{17.64}}$

✒ 22 × 2.52

✒ 55.44 cm²

Now,

Circumference = 2πr

✒ 2 × $\frac{22}{\cancel{7}}$ × ${\cancel{4.2}}$

✒ 2 × 22 × 0.6

✒ 44 × 0.6

✒ 26.4 cm

∴ Area = 55.44 cm² and Circumference = 26.4 cm

✯ Answer 2 :-

Circumference of circle = 44 cm

Also, Circumference = 2πr

✒ 2πr = 44 cm

✒ 2 × $\frac{22}{7}$ × r = 44

✒ r = $\frac{44×7}{2×22}$

✒ r = 7 cm

Now,

Are of circle = πr²

✒ $\frac{22}{7}$ × (7)²

✒ $\frac{22}{\cancel{7}}$ × ${\cancel{49}}$

✒ 22 × 7

✒ 154 cm²

∴ Are if circle is 154 cm²

✯ Answer 3 :-

∅ = 60°

Radius = 6 cm

Now,

Area of sector = $\frac{∅}{360°}$ × πr²

✒ $\frac{\cancel{60°}}{\cancel{360°}}$ × $\frac{22}{7}$ × (6)²

✒ $\frac{1}{\cancel{6}}$ × $\frac{22}{7}$ × ${\cancel{36}}$

✒ 1 × $\frac{22}{7}$ × 6

✒ $\frac{22×6}{7}$

✒ $\frac{\cancel{132}}{\cancel{7}}$

✒ 18.85 cm² ( approx )

∴ Area of sector = 18.85 cm² ( approx )

Answer 2

Answer:

$\tt \red{Question ⤵}</p><p>$

❄️If the radius of a circle is 4.2 cm, compute its area and circumference.

$\tt \red{Solution ⤵}$

Given, Radius (r)= 4.2 cm

$Circumference = \red{ 2\pi \: r}$

$= > \: 2 \times \frac{22}{7} \times 4.2$

$= > ( \frac{44}{10} \times 6) = \frac{246}{10}$

$= > 26.4cm$

Therefore ,

$\tt \: circumference = \pink{ 26.4 cm}$

NOW ,

$Area \: = \red{ \pi \: {r}^{2} }$

$= > \: \frac{22}{7} \times 4.2 \times 4.2$

$\frac{22 \times 6 \times 42}{10 \times 10} = \frac{5544}{100} = 55.44 {cm}^{2}$

Therefore ,

$\tt \: Area = \pink{55.44 {cm}^{2} }$

_______________________________

$\tt \red{Question ⤵}$

❄️ What is the area of a circle whose circumference is 44 cm?

$\tt \red{Solution ⤵}$

Given,

Circumference of circle = 2πr

=> 44 = 2πr

$r = \frac{44}{2\pi} = \frac{44}{2} \times \frac{7}{22} = 7cm$

Now,

$\tt \: Area \: of \: circle = \red {\pi {r}^{2} }$

$= > \frac{22}{7} \times 7 \times 7 = 154 {cm}^{2}$

Hence,

$Area \: of \: circle = \pink{154 {cm}^{2} }$

____________________________&,

$\tt \red{Question ⤵}$

❄️Calculate the area of a sector of angle 60°. Given, the circle is having a radius of 6 cm.

$\tt \red{Solution ⤵}$

Given,

Radius = r = 6 cm

& angle of the sector = 60°

We know that,

$Area \: of \: the \: sector = \frac{θ}{360°} \times \pi {r}^{2}$

$= > \frac{60}{360} \times \frac{22}{7} \times ( {6)}^{2}$

$= > \frac{1}{6} \times \frac{22}{7} \times 36$

$= > \frac{132}{7} {cm}^{2}$