Question

The radius of circle is 4m and what is the radius of another circle area is 16 times of first

Answer 1

$\huge\mathbb{SOLUTION:-}$

Given :-

The radius of 1 circle is 4m

$\huge\sf{To\:Find}$

• The radius of circle area is 16 times the 1st circle whose radius is 4m

$\bf\underline{\underline{Step\:By\:step\: Explanation:-}}$

• First find the area of circle 1

$\boxed{\sf{Area\:of\:circle=\pi r{}^{2}}}$

$\sf\implies Area\:of\:circle_1=\frac{22}{7}\times (4m){}^{2}\\ \\ \sf\implies Area\:of\:circle_1=\frac{22}{7}\times 16\\ \\ \sf\implies Area\:of\:circle_1=\frac{352}{7}cm{}^{2}$

$\boxed{\sf{Area\:of\:circle_1=\frac{352}{7}cm{}^{2}}}$

• Now the area of 2nd circle is 16 times the area of 1st circle

• if we multiply 16 to the area of 1st circle we get the area of 2nd circle

$\boxed{\sf{ Area\:of\: circle_2=16\times Area\:of\:circle_1}}$

$\sf \longrightarrow \pi r{}^{2}=16\times \frac{352}{7}\\ \\ \sf\implies \frac{22}{7}\times r{}^{2}=\frac{16\times 352}{7}\\ \\ \sf\implies r{}^{2}=\frac{16\times 352}{\cancel7}\times \frac{\cancel7}{22}\\ \\ \sf\implies r{}^{2}=\frac{16\times \cancel{352}}{\cancel{22}}\\ \\ \sf\implies r{}^{2}=16\times 16\\ \\ \sf\implies radius=\sqrt{16\times 16}\\ \\ \sf\implies radius\:of\:circle_2=16cm$

$\boxed{\sf{Radius\:of\:new\:circle=16cm}}$

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Answer 2

Given :----

• Radius of circle = 4m

To Find :----

• Radius of another circle whose area is 16 times of First ...

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Solution (1)

We know that, area of circle = πr² (with radius r)

→ putting value we get, area = π(4)² = 16π m²

Now, it is said that, Area of another circle is 16 times of First circle .

so,

→ Area of second circle = 16(16π) m² = 256π m²

Now, we have to Find radius of this circle.

Again comparing area of circle we get,

==>> πr² = 256π

==>> r² = 256

==>> r² = 16*16

==>> r = 16m.

Hence, radius of another circle will be 16m .

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Solution (2)

Area of circle with radius r1 and r2 is given by (r1)² : (r2)²

Here , in Question Area of both circle is given by = 1:16

so,

putting we get,

→ (r1)² : (r2)² = 1 : 16

→ (r1)² : (r2)² = (1)² : (4)²

→ (r1) : (r2) = 1 : 4

Given that r1 is = 4m

Hence, r2 = 4*4 = 16m ..

so, radius of another circle will be 16m .

(No need of Extra calculation Required)

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#BAL

#answerwithquality