Question

The diameter of a circle field is 40m and that of another 96m . find the diameter of the circular field whose area is equal to the sum of the area of two fields ​

Answer 1

• Diameter of the circular field=40 m
• 
  `r = \displaystyle{ (40 \: m)/(2)}`
• 
  `r=20 m`
• Diameter of another circular field=
  `96 m`
• r=
  `\displaystyle{(96 m)/(2)}`
• r=48 m

Area of circular field(2)=
`πr^2`

=
`π×(20)^2`

=
`400π`

Area of circular field(2)=
`πr^2`

=
`π×(48)^2`

=
`2304π`

• The sum of the area of the two fields=
  `400π+2304π`
• =
  `2704π`

Let the radius of circular field that is formed so be r meter(m).

Now,

`\cancel\pi {r}^(2) = 2704 \cancel\pi`

`{r}^(2) = 2704`

`r = √(2704)`

`r = 52 \: m`

• Area of the circular field whose area is equal to the areas of two fields,

Diameter=
`2r`

Diameter=
`2×52`

Diameter=
`104 m`

• The diameter of the circular field whose area is equal to the areas of two fields is 104 m.

Explanation:

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Answer 2

According to the Question

Diameter of a circle field is 40m and that of another 96m .

We have to find the diameter of the circle whose area is equal to the sum of the area of given two circular fields.

Radius of field whose diameter is 40 m

→ r = 40/2 = 20m

Radius of field whose diameter is 96 m

→ r' = 96/2 = 48m

Now, calculating the diameter of Larger circular field.

Let the radius of larger field be R m .

Now, according to the given statement

Sum of Area of given two circular fields = Area of larger field

➠ πr² + πr'² = πR²

➠ π ( r² + r'²) = π R²

➠ 20² + 48² = R²

➠ 400 + 2304 = R²

➠ 2704 = R²

➠ √2704 = R

➠ 52 = R

Therefore, Diameter = 2 × R = 2×52 = 104 m

So, the diameter of Larger circular field is 104 m .