Question

Find the diameter of a circle and its circumference if its area is 25π cm².​

Answer 1

Answer :-

• The diameter of circle is 10cm.
• The circumference of circle is 31.42cm.

Step-by-step explanation:

To Find :-

• The diameter of circle
• The circumference of circle

Solution:

Given that,

• Area of circle = 25π cm²

Therefore,

$\tt{\longmapsto \: \purple{Area \: of \: circle = \pi \: {(r)}^{2}}} \\ \\ \tt{\longmapsto \: 25\pi = \pi \: {(r)}^{2}} \\ \\ \tt{\longmapsto \: 25 \cancel{\pi} = \cancel{\pi} \: {(r)}^{2}} \\ \\ \tt{\longmapsto \: 25 = {(r)}^{2}} \\ \\ \tt{\longmapsto \: \sqrt{25} = r} \\ \\ \tt{ \longmapsto \: 5 = r} \: \bigstar \\ \underline{\sf{Hence,\: The \: radius \: of \: circle \: is \: 5cm}}$

According the question,

• The diameter of circle

$\rm{As \: we \: know \: that,} \\ \\ \bf{Diameter \: of \: circle = 2 \times radius}$

Therefore,

$\tt{\longmapsto \: (2 \times 5)cm} \\ \\ \tt{\longmapsto \: 10cm}$

Hence, The diameter of circle is 10cm.

• The circumference of circle

$\rm{As \: we \: know \: that,} \\ \\\bf{Circumference \: of \: circle = 2\pi \: r}$

Therefore,

$\tt{\longmapsto \: 2 \times \dfrac{22}{7} \times 5} \\ \\ \tt{\longmapsto \: \dfrac{2 \times 22}{7} \times 5} \\ \\ \tt{\longmapsto \: \dfrac{44}{7} \times 5} \\ \\ \tt{\longmapsto \: \dfrac{44 \times 5}{7}} \\ \\ \tt{\longmapsto \: \dfrac{220}{7}} \\ \\ \tt{\longmapsto \: \cancel{\dfrac{220}{7}}} \\ \\ \tt{\longmapsto \: 31.42} \: \bigstar \: \\ \underline{\sf{Hence,\: The \: circumference \: of \: circle \: is \: 31.42cm}}$

Hence, The circumference of circle is 31.42cm.