Question

please tell me please​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Central angle of the sector is}\;\mathsf{15^{\circ}}$

$\textsf{and area of the sector 231 square cm}$

$\underline{\textsf{To find:}}$

$\textsf{Circumference of the circle}$

$\underline{\textsf{Solution:}}$

$\textsf{As per given data,}$

$\textsf{Area of the sector=231 square cm}$

$\implies\mathsf{\dfrac{\theta}{360^{\circ}}{\times}\pi\,r^2}=231}$

$\implies\mathsf{\dfrac{15^{\circ}}{360^{\circ}}{\times}\dfrac{22}{7}{\times}r^2=231}$

$\implies\mathsf{\dfrac{1}{24}{\times}\dfrac{22}{7}{\times}r^2=231}$

$\implies\mathsf{\dfrac{1}{12}{\times}\dfrac{11}{7}{\times}r^2}=231}$

$\implies\mathsf{\dfrac{1}{12}{\times}\dfrac{1}{7}{\times}r^2=21}$

$\implies\mathsf{r^2=21{\times}7{\times}12}$

$\implies\mathsf{r^2=3{\times}7{\times}7{\times}3{\times}4}$

$\implies\mathsf{r^2=3^2{\times}7^2{\times}2^2}$

$\implies\mathsf{r=3{\times}7{\times}2}$

$\implies\mathsf{r=42\;cm}$

$\textsf{Now}$

$\textsf{Circumference of the circle}$

$\mathsf{=2\,\pi\,r}$

$\mathsf{=2{\times}\dfrac{22}{7}{\times}42}$

$\mathsf{=2{\times}22{\times}6}$

$\mathsf{=44{\times}6}$

$\mathsf{=264\;square\;cm}$

$\underline{\textsf{Answer:}}$

$\textsf{Circumference of the circle is 264 square cm}$

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Answer 2

Question :- The area of a sector , with central angle 15° of a circle is 231cm² . if π = (22/7) , what is the the circumference(in cm) of the circle ?

Solution :-

we know that,

• Area of sector with central angle as θ , and radius of circle as r is = (θ/360°) * π * (r)² .

given that,

• θ = 15°
• Area of sector = 231 cm².
• radius of circle = Let r.

Putting values we get,

→ (θ/360°) * π * (r)² = 231

→ (15°/360°) * (22/7) * r² = 231

→ (1/24) * (22/7) * r² = 231

→ 22 * r² = 231 * 7 * 24

dividing both sides by 2,

→ 11 * r² = 231 * 7 * 12

dividing both sides by 11,

→ r² = 21 * 7 * 12

→ r² = (7 * 7) * (3 * 3) * 4

→ r² = (7² * 3² * 2²)

→ r² = (7 * 3 * 2)²

→ r² = (42)²

square root both sides,

→ r = 42 cm.

Therefore ,

→ circumference of the circle = 2 * π * radius .

→ circumference of the circle = 2 * (22/7) * 42

→ circumference of the circle = 44 * 6

→ circumference of the circle = 264 cm . (Ans.)

Hence, circumference of the circle is 264 cm.

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