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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 ​

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Answer :

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 .

Answer:

  • Diameter of the circular field=40 m
  • [tex]r = \displaystyle{ \frac{40 \: m}{2}} [/tex]
  • [tex]r=20 m[/tex]
  • Diameter of another circular field=[tex]96 m[/tex]
  • r=[tex]\displaystyle{\frac{96 m}{2}}[/tex]
  • r=48 m

Area of circular field(2)=[tex]πr^2[/tex]

=[tex]π×(20)^2[/tex]

=[tex]400π[/tex]

Area of circular field(2)=[tex]πr^2[/tex]

=[tex]π×(48)^2[/tex]

=[tex]2304π[/tex]

  • The sum of the area of the two fields=[tex]400π+2304π[/tex]
  • =[tex]2704π[/tex]

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

Now,

[tex] \cancel\pi {r}^{2} = 2704 \cancel\pi[/tex]

[tex] {r}^{2} = 2704[/tex]

[tex]r = \sqrt{2704} [/tex]

[tex]r = 52 \: m[/tex]

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

Diameter=[tex]2r[/tex]

Diameter=[tex]2×52[/tex]

Diameter=[tex]104 m[/tex]

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

Step-by-step explanation:

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