Question

It is proposed to build a single park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be ______.

Answer 1

It is proposed to build a single park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. The radius of the new park would be 10 m.

Explanation:

Radii = `16/2` = 8 m and `12/2` = 6 m. 

Sum of areas = π(8²) + π(6²)

= 64π + 36π

= 100π

If πR² = 100π,

Then R² = 100 

⇒ R = 10 m