1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
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 ___________.

Open in App
Solution

## Let the radius of the new circular park be r m. Suppose the radii of two circular parks be r1 m and r2 m. Diameter of the first circular park = 16 m ⇒ 2r1 = 16 ⇒ r1 = 8 m Diameter of the second circular park = 12 m ⇒ 2r2 = 12 ⇒ r2 = 6 m Now, Area of the new circular park = Area of first circular park + Area of second circular park $\mathrm{\pi }{r}^{2}=\mathrm{\pi }{r}_{1}^{2}+\mathrm{\pi }{r}_{2}^{2}\phantom{\rule{0ex}{0ex}}⇒{r}^{2}={r}_{1}^{2}+{r}_{2}^{2}\phantom{\rule{0ex}{0ex}}⇒{r}^{\mathit{2}}={\left(8\right)}^{2}+{\left(6\right)}^{2}\phantom{\rule{0ex}{0ex}}⇒{r}^{\mathit{2}}=64+36=100$ $⇒r=\sqrt{100}$ = 10 m Thus, the radius of the new park is 10 m. 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__.

Suggest Corrections
2
Join BYJU'S Learning Program
Related Videos
Circumference of Circle
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program