Question

The ratio of areas of two circular paintings is 16:25. If the radius of the smaller painting is 4 feet what will be the radius of the larger one? ​

Answer 1

Answer:

$\huge\blue{5}$

Step-by-step explanation:

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Let the radii of the circles be r1 & r2 respectively.

Then, their circumferences are 2πr1 & 2πr2, respectively.

So, their ratio=2πr1:2πr2=r1:r2.

Again, the areas of the circles are π(r1)2 & π(r2)2.

Then, their ratio =π(r1)2:π(r2)2=(r1)2:(r2)2=16:25 ...(given).

∴(r1):(r2)=√16:25

=±(4:5)

We reject the negative value of r's since the radius is a length.

∴(r1):(r2)=(4:5).

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Answer 2

Answer:

5

Step-by-step explanation:

The area of smaller painting is 3.14×4²= 50.24 (πr²)

let the area of larger painting be 3.14×r²

then

$\frac{50.24}{3.14 \times {r}^{2} } = \frac{16}{25}$

${r}^{2} \times 50.24 = 1256 \\ {r}^{2} = 1256 \div 50.24 \\ {r }^{2} = 25 \\ r = 5$