Question

A circular fish pond has a diameter of 14 m. The pond is surrounded by a concrete path 1.75m
wide. Then the area of the path
1) 86.7237
2) 86.675m 3) 86.545m
4) 86.4547​

Answer 1

$\large{\pmb{\mathfrak{\underline{\purple{Given...}}}}}$

Given that :

• Diameter of a fish pond =$\sf 14m$
• Width of the concrete path surrounding the pond = $\sf 1.75m$

$\large {\pmb{\mathfrak{\underline{\purple{To~ find...}}}}}$

We should find the area of the path.

$\large{\pmb{\mathfrak{\underline{\purple{Solution...}}}}}$

Here,

• Diameter of the pond = $\sf 14m$
• Radius of the pond = $\sf 7m$

${\bf{\orange{Area~ of~ a~ circle=\pi r^2}}}$

Finding area of inner circle :

$\sf :\implies Area_{(inner~circle)}=(\dfrac{22}{7})(7m)(7m)$

$\sf :\implies Area_{(inner~circle)}=(\dfrac{22}{\cancel7})(\cancel7 m)(7m)$

$\sf :\implies Area_{(inner~circle)}=(22)(7m)$

${\bf{\orange{ Area_{(inner~ circle)}=154m^2}}}$

Now,

• Width of the concrete path surrounding the pond = $\sf 1.75m$
• Radius of outer circle = Radius of inner circle + Width of the path
• Radius of outer circle = $\sf 8.75m$

${\bf{\orange{Area~ of~ a~ circle=\pi r^2}}}$

Finding area of outer circle :

$\sf :\implies Area_{(outer~ circle)}=(\dfrac{22}{7})(8.75m)(8.75m)$

$\sf :\implies Area_{(outer~ circle)}=(\dfrac{22}{\cancel7})(\cancel{8.75}m)(8.75m)$

$\sf :\implies Area_{(outer~ circle)}=(22)(1.75m)(8.75m)$

${\bf{\orange{Area_{(outer~ circle)}=240.625m^2}}}$

Finally,

Finding the area of the path :

${\bf{\orange{Area_{(path)}=Area_{(outer~ circle)}-Area_{(inner~ circle)}}}}$

$\sf :\implies Area_{(path)}=240.625m^2-154m^2$

$\sf{ Area_{(path)}= 86.625m^2}$

_______________________

${\orange{\therefore{\pmb{\bf{Area~of~the~ concrete~path~is~ 86.625m^2.}}}}}$