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

Answer:

• Diameter of the circular field=40 m
• $r = \displaystyle{ \frac{40 \: m}{2}}$
• $r=20 m$
• Diameter of another circular field=$96 m$
• r=$\displaystyle{\frac{96 m}{2}}$
• 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,

$\cancel\pi {r}^{2} = 2704 \cancel\pi$

${r}^{2} = 2704$

$r = \sqrt{2704}$

$r = 52 \: m$

• 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.

Step-by-step explanation:

$\frak{ \blue{DisneyPrincess29}}$

Answer 2

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 .