Question

the area of a circular tin plate is 31.5 cm​, find the circumference

Answer 1

Answer:

Appropriate Question :-

• The area of a circular tin plate is 31.5 cm². Find the circumference of a circular tin plate.

Given :-

• The area of a circular tin plate is 31.5 cm².

To Find :-

• What is the circumference of a circular tin plate.

Solution :-

First, we have to find the radius of a circular tin plate :

Given :

• Area of a circular tin plate = 31.5 cm²

According to the question by using the formula we get,

$\implies \sf\boxed{\bold{\pink{Area_{(Circle)} =\: {\pi}r^2}}}$

$\implies \sf 31.5 =\: \dfrac{22}{7} \times r^2$

$\implies \sf 31.5 \times \dfrac{7}{22} =\: r^2$

$\implies \sf \dfrac{220.5}{22} =\: r^2$

$\implies \sf 10.02 =\: r^2$

$\implies \sf \sqrt{10.02} =\: r$

$\implies \sf 3.16 =\: r$

$\implies \sf\bold{\purple{r =\: 3.16}}$

Hence, the radius of a circular tin plate is 3.16 cm .

Now, we have to find the circumference of a circular tin plate :

Given :

• Radius = 3.16 cm

According to the question by using the formula we get,

$\small \implies \sf\boxed{\bold{\pink{Circumference_{(Circle)} =\: 2{\pi}r}}}$

$\small \implies \sf Circumference_{(Circular\: Tin\: Plate)} =\: 2 \times \dfrac{22}{7} \times 3.16$

$\small \implies \sf Circumference_{(Circular\: Tin\: Plate)} =\: \dfrac{44}{7} \times 3.16$

$\small \implies \sf Circumference_{(Circular\: Tin\: Plate)} =\: \dfrac{139.04}{7}$

$\small \implies \sf\bold{\red{Circumference_{(Circular\: Tin\: Plate)} =\: 19.86\: cm}}$

$\therefore$ The circumference of a circular tin plate is 19.86 cm .