Question

A circular water fountain 6.6 m in diameter is surrounded by a path of width 1.5 m. The area of this path?

Answer 1

Answer:

Area of the path = 38.15 m²

Step-by-step explanation:

Diameter of fountain, d = 6.6 m

Area of fountain = πd²/4 = 3.14*6.6²/4 = 34.20 m²

Width of path = 1.5m

Diameter of circle including fountain and path, D = 1.5 + 6.6 + 1.5 = 9.6 m

Area of circle including fountain and path = πD²/4

= 3.14*9.6²/4 = 72.35 m²

Area of the path = 72.35 - 34.20 = 38.15 m²

Answer 2

$\green {╔═════════════════════╗}$

$\blue {⇰Diameter = 6.6m}$

$\sf ⇒\dfrac{6.6}{2} m$

$\sf ⇒3.3m$

$\pink {⇰Area \: of \: the \: fountain \: = \pi d^{2}}$

$\sf ➩\dfrac{22}{7} \times (3.3m {)}^{2}$

$\sf ➩\dfrac{22}{7} \times 3.3m \times 3.3m$

$\sf ➩\dfrac{ \cancel2 \cancel {2}^{11} }{7} \times \dfrac{33}{ \cancel 1 \cancel {0}^{5} } \times \dfrac{33}{10}$

$\sf ➩\dfrac{11979}{350}$

$\sf ➩34.22$

$\orange {⇰Diameter \: of \: bigger \: circle}$

$\sf ➯6.6m + 1.5m + 1.5m$

$\sf ➯9.6m$

$\purple {⇰Radius \: of \: bigger \: circle}$

$\sf ➬\dfrac{ \cancel9. \cancel {6}^{4.8} }{2} m$

$\sf ➬4.8m$

$\red {⇰Area \: of \: bigger \: circle = \pi {r}^{2}}$

$\sf ➾\dfrac{22}{7} \times (4.8m {)}^{2}$

$\sf ➾\dfrac{ \cancel2 \cancel {2}^{11} }{7} \times \dfrac{\cancel4\cancel {8}^{24} }{\cancel1\cancel {0}^{5} } \times \dfrac{48}{ \cancel1\cancel {0}^{5} }$

$\sf ➾\dfrac{12672}{175} m$

$\sf ➾72.41m$

$\green {Area \: of \: the \: path = 72 . 41 - 34.22}$

$\sf ➺38.19m$

$\blue {╚═════════════════════╝}$