Question

Find the area of circular Ring if outer diameter D=38mm, inner diameter d =32mm

Answer 1

Answer: The answer is 330 mm^2

Step-by-step explanation:

Answer 2

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Question :-

Find the area of a circular ring if the outer diameter (D) = 38 mm , inner diameter (d) = 32 mm .

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Answer :-

Given :-

Outer diameter (D) = 38 mm

Inner diameter (d) = 32 mm

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Required to find :-

• Area of the ring ?

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Formulae used :-

$\underline{\boxed{\orange{\tt{Radius = \dfrac{Diameter}{2}}}}}$

$\underline{\boxed{\red{\mathrm{Area \; of \; a \; ring = \pi ( ({R}_{1}{)}^{2} - ({R}_{2}{)}^{2} )}}}}$

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Solution :-

In the question it is given that,

Outer diameter (D) = 38 mm

Inner diameter (d) = 32 mm

And he asked us to find the area of the ring .

In order to find the area of the ring ,

we should first find the length of the radius .

So, here we should use the formula .

The formula is ,

$\underline{\boxed{\orange{\tt{Radius = \dfrac{Diameter}{2}}}}}$

Using this formula we can find the length of the radius ,

Here,

Outer diameter (D) = 38 mm

so,

Outer radius = ?

=> 38/2

=> 19 mm

So, Outer radius (R1) = 19 mm

Similarly,

Inner diameter (d) = 32 mm

So,

Inner radius = ?

=> 32/2

=> 16 mm

So, inner radius (R2) = 16 mm

Now, here we have to use a formula to find the area of the ring .

The formula is

$\underline{\boxed{\red{\mathrm{Area \; of \; a \; ring = \pi ( ({R}_{1}{)}^{2} - ({R}_{2}{)}^{2} )}}}}$

Here, substitute the respective values .

( value of π (pi) = 22/7 )

We get,

$\longrightarrow{\tt{ Area = \dfrac{22}{7} \times ( {(19)}^{2} - {(16)}^{2} )}}$

$\longrightarrow{\tt{ Area = \dfrac{22}{7} \times ( 361 - 256 ) }}$

$\longrightarrow{\tt{ Area = \dfrac{22}{7} \times 105 }}$

$\longrightarrow{\tt{ Area = 22 \times 15 }}$

$\red{\underline{\implies{\tt{ Area = 330 {mm}^{2}}}}}$

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Therefore,

Area of the ring = 330 mm²

Note :

If the value of pi is taken as 3.14 the value which we get is 329.87 which is actually equal to 330 mm² approximately

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Points to remember :-

1. In a ring we have 2 radii ,

1. Inner radius
2. Outer radius

2. please refer to the attachment given

3. Refer the formulae mentioned above

4. Diameter is actually two times the radius

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