Question

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i) Find the area of a circular pond that has a diameter of 12m.
ii)The pond is surrounded by a path of width 2m. If the costs $55 per square meter to pave the path with tiles, find the cost incurred.
Give step by step explanation please.​
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Answer 1

Given :

• Diameter of the circular pond = 12m
• Radius of the circular pond = D/2 = 12/2 = 6m
• Width of the path = 2m

To find :

• Area of the pond?
• Cost incurred?

Solution :

~As we know that,

• Area of circle = πr²

➟ Area of pond = 3.14 × 6 × 6

➟ Area of pond = 113.04 m²

•°• The area of the circular pond is 113.04 m².

Now, it is given that the pond is surrounded by a path of width 2m.

➟ Radius of the pond with path = 6 + 2

➟ Radius of the pond with path = 8m

Therefore,

➟ Area of the pond with path = 3.14 × 8 × 8

➟ Area of the pond with path = 200.96 m²

➟ Area of path = (200.96 – 113.04)

➟ Area of path = 87.92 m²

Now, cost incurred,

➟ Area of pond with path × Total cost

➟ 87.92 × 55

➟ $4835.6

•°• The cost incurred to pave the path with tiles is $4835.6.

Answer 2

(i) Find the area of a circular pond that has a diameter of 12m.

GIVEN :-

Diameter of pond = 12 m

TO FIND :-

Area of a circular pond.

SOLUTION :-

We know that,

$\fbox {\sf Radius = \frac{Diameter}{2}}$

$\sf r = \frac{12}{2} = 6 \: m$

We know also that,

$\fbox{\sf Area \: of \: circle = {\pi r}^{2}}$

$\sf = \pi \times {6}^{2}$

$\sf = 3.14 \times 6 \times 6$

$\sf = 3.14 \times 36$

$\fbox\orange{ \sf = {113.04 \: m}^{2}}$

∴ Hence Area of circular pond is 113.04 m².

(ii) The pond is surrounded by a path of width 2m. If the costs $55 per square meter to pave the path with tiles, find the cost incurred.

GIVEN :-

Width of path = 2 m

TO FIND :-

Cost of tiling the path.

SOLUTION :-

☞ Radius of pond with path =

$\fbox{ \sf Radius + Width \: of \: path}$

$\sf =6m + 2m$

$\sf =8m$

Then,

☞ Area of pond with path = $\sf {\pi r}^{2}$

$\sf = 3.14 \times 8 \times 8$

$\sf = 3.14 \times 64$

$\sf = {200.96m}^{2}$

Therefore,

Area of path = $\fbox{\sf Area \: of \: pond \: with \: path - Area \: of \: pond}$

$\sf 200.96 - 113.04$

${\sf = {87.92m}^{2}}$

∴ $\fbox{ \sf Total \: cost = Rate × Area \: of \: path}$

$\sf = 55 \times 87.92$

$\fbox\orange{ \sf = Dollar \: 4835.6}$

∴ Cost of tiling path is $ 4835.6.

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$\fbox \green{ \sf Thank You!!!}$