Question

What is the diameter of a circle with area 314 sq.cm?
Select one:
a. 15
b. 5
C. 20
d. 10​

Answer 1

Given:

• Area of Circle = 314 cm²

To find:

• Diameter of circle?

Solution:

☯ Let radius of circle be r cm.

We know that,

★ Area of Circle = πr²

Now, Putting value,

⇒ 3.14 × r² = 314

⇒ r² = 100

⇒ r² = (10)²

⇒√r² = √10²

⇒ r = 10 cm

Thus, Radius of circle is 10 cm.

We know that,

• Diameter of circle = 2 × Radius

∴ Diameter of circle is 20 cm.

Hence, Option (D) is correct.

⠀━━━━━━━━━━━━━━━━━━━━━━━

More to know:

• Circumference of Circle = 2πr

• Area of sector = θ/360 × πr²

• Length of an arc = θ/360 × 2πr

Answer 2

Answer:

$\large \bigstar\bf {\underbrace \color{navy}{ \: \: \: \: \: \: \: \: \: \: given- \: \: \: \: \: \: \: \: \: \: } }\bigstar$

• Area of Circle = 314 cm²

$\large \bigstar\bf {\underbrace \color{navy}{ \: \: \: \: \: \: \: \: \: \: To \:find- \: \: \: \: \: \: \: \: \: \: } }\bigstar$

• Diameter of the circle = ?

$\large \bigstar\bf {\underbrace \color{navy}{ \: \: \: \: \: \: \: \: \: \: Formula-\: \: \: \: \: \: \: \: \: \: } }\bigstar$

$\\ \bigstar\bf \underline{\color{lime}{area \: of \:a \: circle = \pi r {}^{2}}}\bigstar$

$\large \bigstar\bf {\underbrace \color{navy}{ \: \: \: \: \: \: \: \: \: \: Solution- \: \: \: \: \: \: \: \: \: \: } }\bigstar$

$\\ \implies \sf \green{3.14 \times {r}^{2} = 314 } \\ \implies \sf \green{ {r}^{2} = \cancel\frac{ 314 }{3.14} } \\ \implies \sf \green{ {r}^{2} = 100} \\ \implies \sf \green{ {r}^{2} = (10) {}^{2} } \\ \implies \sf \green{ \sqrt{r {}^{2} } = \sqrt{10 {}^{2} } } \\ \implies \sf \green{r = 10} \\ \\ \therefore \bf \pink{ radius \: of \: circle = 10}$

$\large \bigstar\bf {\underbrace \color{navy}{ \: \: \: \: \: \: \: \: \: \: Now\:formula+\: \: \: \: \: \: \: \: \: \: } }\bigstar$

$\bf {\fbox\color{brown}{diameter \: of \: a\: circle = 2 radius}}$

$\\ \bf \underline\red{diameter \: of \: a \: circle = 2 \times 10} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \underline \red{ \: \: = 20 \: \: \: \: }$