Question

v) If difference between circumference and diameter of a circle is 56 cm, then the radius of the circle is?

help please​

Answer 1

Answer :-

$\\\;\large{\underbrace{\underline{\textsf{Question's Analysis :-}}}}$

The above question is simply based on Circle. Here the concept of Circumference of a Circle and Diameter of a Circle have been used. The difference between Circumference and Diameter of Circle is 56cm, according to the question. We are meant to work out the Circle's radius. We can use the stated condition to find the Radius of the Circle.

Let's do it !!

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Knowledge required :-

A circle is a closed plane geometric shape figure. It is always lie at the same distance from a focal/center point.

The circumference of a circle is the product of 2, pi and length of the radius of a circle.

The diameter is twice the length of the radius of a circle.

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Formulas used :-

$\\\;\boxed{\sf{\;Circumference_{(Circle)}=\bf{2\pi{r}}\;}}$

$\\\;\boxed{\sf{\;Diameter_{(Circle)}=\bf{\pi{r}}\;}}$

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Solution :-

The difference between Circumference and Diameter of Circle is 56cm. Soz we can form the equation as;

$\\\;:\implies\;\tt{Circumference_{(Circle)} - Diameter_{(Circle)} = 56}$

$\\\;:\implies\;\tt{2\pi r - 2r = 56}$

$\\\;:\implies\;\tt{2r(\pi - 1) = 56}$

$\\\;:\implies\;\tt{r(\pi - 1) = \dfrac{56}{2}}$

$\\\;:\implies\;\tt{r(\pi - 1) = 28}$

$\\\;:\implies\;\tt{r\left(\dfrac{22}{7} - 1\right) = 28}$

$\\\;:\implies\;\tt{r\left(\dfrac{22-7}{7}\right) = 28}$

$\\\;:\implies\;\tt{r\left(\dfrac{15}{7}\right) = 28}$

$\\\;:\implies\;\tt{\dfrac{15}{7}r = 28}$

$\\\;:\implies\;\tt{\dfrac{15r}{7} = 28}$

$\\\;:\implies\;\tt{15r=28\times7}$

$\\\;:\implies\;\tt{15r=196}$

$\\\;:\implies\;\tt{r=\dfrac{196}{15}}$

$\\\;:\implies\;\red{\boxed{\bf{\blue{r=13.06}}}}$

Thus, the radius of the circle is 13.06cm.

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More to know :-

• A Circle is a closed plane geometric shape figure.

• The diameter of a circle is the longest chord of a circle.

• The radius drawn perpendicular to the chord bisects the chord.

• A Circle is always lie at an equal distance from a center point.

• Circles having different radius are similar.

• The radius is half of the diameter. i.e. r = D/2.

• The diameter is twice the length of the radius of a circle. i.e. D = 2r.

• The circumference of a circle is the product of pi and length of the diameter of a circle. i.e. C = πD.

• The area of a circle is pi times the radius squared. i.e. A = πr².

Answer 2

Answer:

Given :-

• The difference between circumference and diameter of a circle is 56 cm.

To Find :-

• What is the radius of the circle.

Formula Used :-

$\clubsuit$ Circumference Of Circle Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Circumference_{[Circle]} =\: 2{\pi}r}}}\: \: \: \bigstar$

$\clubsuit$ Diameter Of Circle Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Diameter_{[Circle]} =\: 2r}}}\: \: \: \bigstar$

where,

• π = Pie or 22/7
• r = Radius

Solution :-

Let,

$\mapsto \bf Radius_{(Circle)} =\: r\: cm$

Given :

• Difference between circumference and diameter = 56 cm

According to the question by using the formula we get,

$\bigstar$ The difference between the circumference and diameter of a circle is 56 cm.

So,

$\small \implies \sf\bold{\blue{\bigg\{Circumference_{[Circle]}\bigg\} - \bigg\{Diameter_{[Circle]}\bigg\} =\: 56}}$

$\implies \bf 2{\pi}r - 2r =\: 56$

$\implies \sf 2r\bigg[{\pi} - 1\bigg] =\: 56$

$\implies \sf r\bigg[{\pi} - 1\bigg] =\: \dfrac{\cancel{56}}{\cancel{2}}$

$\implies \sf r\bigg[{\pi} - 1\bigg] =\: \dfrac{28}{1}$

$\implies \sf r\bigg[{\pi} - 1\bigg] =\: 28$

$\implies \sf r\bigg[\dfrac{22}{7} - 1\bigg] =\: 28$

$\implies \sf r\bigg[\dfrac{22 - 7}{7}\bigg] =\: 28$

$\implies \sf r\bigg[\dfrac{15}{7}\bigg] =\: 28$

$\implies \sf r \times \dfrac{15}{7} =\: 28$

$\implies \sf \dfrac{r \times 15}{7} =\: 28$

$\implies \sf \dfrac{15r}{7} =\: 28$

$\implies \sf 15r =\: 28(7)$

$\implies \sf 15r =\: 28 \times 7$

$\implies \sf 15r =\: 196$

$\implies \sf r =\: \dfrac{196}{15}$

$\implies \sf\bold{\green{r =\: 13.067}}$

Hence, the required radius of a circle is :

$\dashrightarrow \sf Radius_{(Circle)} =\: r\: cm$

$\dashrightarrow \sf\bold{\red{Radius_{(Circle)} =\: 13.067\: cm}}$

$\sf\bold{\purple{\underline{\therefore\: The\: radius\: of\: the\: circle\: is\: 13.067\: cm\: .}}}$

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