Question

the circular path is outside the circular garden. if its external circumference is 508m and internal circumference is 420 m. what is the area of the path​

Answer 1

Answer:

Gɪᴠᴇɴ :-

♱External Circumference = 508m

♱Internal Circumference = 420m

Fɪɴᴅ :-

⚚Area of the path

Sᴏʟᴜᴛɪᴏɴ:-

For outer circle

we, know that

$\huge{\underline{\boxed{\sf Circumference \: of \: circle = 2 \pi r}}}$

where,

• Circumference of outer circle = 508m

• π = 22/7

So,

$\begin{lgathered}\dashrightarrow \sf Circumference_{outer \: circle}= 2 \pi r \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow \sf 508= 2 \times \dfrac{22}{7} r \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow \sf 508=\dfrac{44}{7} r \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow \sf 508 \times \dfrac{7}{44} =r \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow \sf \dfrac{3556}{44} =r \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow \sf 80.818(approx.) m=r \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow \sf 80.8m=r \\ \\\end{lgathered}$

$\begin{lgathered}\therefore \sf radius_{outer \: circle} = 80.8m\\ \\\end{lgathered}$

Now, using

$\huge{\underline{\boxed{\sf Area \: of \: circle =\pi r^2}}}$

where,

• Radius of outer circle = 80.8m

So,

$\begin{lgathered}\dashrightarrow\sf Area_{outer \: circle}=\pi r^2 \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow\sf Area_{outer \: circle}= \dfrac{22}{7} \times (80.8)^2 \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow\sf Area_{outer \: circle}= \dfrac{22}{7} \times 6528.64 \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow\sf Area_{outer \: circle}= \dfrac{143630.08}{7} \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow\sf Area_{outer \: circle}=20518.582 {m}^{2} (approx.) \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow\sf Area_{outer \: circle}=20518.6 {m}^{2} \\ \\\end{lgathered}$

$\begin{lgathered}\small{\therefore\sf Area_{outer \: circle}=20518.6 {m}^{2}} \\ \\\end{lgathered}$

Now, for inner circle

$\huge{\underline{\boxed{\sf Circumference \: of \: circle = 2 \pi r}}}$

where,

• Circumference of inner circle = 420m

So,

$\begin{lgathered}\dashrightarrow \sf Circumference_{inner \: circle}= 2 \pi r \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow \sf 420= 2 \times \dfrac{22}{7} r \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow \sf 420= \dfrac{44}{7} r \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow \sf 420 \times \dfrac{7}{44} = r \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow \sf \dfrac{2940}{44} = r \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow \sf 66.818m(approx.)= r \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow \sf 66.82m= r \\ \\\end{lgathered}$

$\begin{lgathered}\therefore\sf radius_{inner \: circle}= 66.82m\\ \\\end{lgathered}$

Again, using

$\huge{\underline{\boxed{\sf Area \: of \: circle =\pi r^2}}}$

where,

• Radius of Inner Circle = 66.82m

So,

$\begin{lgathered}\dashrightarrow\sf Area_{inner\: circle}=\pi r^2 \\ \ \end{lgathered}$

$\begin{lgathered}\dashrightarrow\sf Area_{inner\: circle}= \dfrac{22}{7} \times (66.82)^2 \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow\sf Area_{inner\: circle}= \dfrac{22}{7} \times 4464.9124 \\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow\sf Area_{inner\: circle}= \dfrac{98228.0728}{7}\\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow\sf Area_{inner\: circle}= 14032.581m^2(approx.)\\ \\\end{lgathered}$

$\begin{lgathered}\dashrightarrow\sf Area_{inner\: circle}= 14032.58m^2\\ \\\end{lgathered}$

$\begin{lgathered}\therefore\sf Area_{inner\: circle}= 14032.58m^2\\ \\\end{lgathered}$

Nᴏᴡ,

➙Area of path = Area of outer circle - Area of Inner Circle

▶20518.6m² - 14032.58m²

▶6486.02m²

Hence, Area of the path is 6486.02m²

☘Tʜᴀɴᴋs!!

Answer 2

Step-by-step explanation:

Gɪᴠᴇɴ :-

♱External Circumference = 508m

♱Internal Circumference = 420m

Fɪɴᴅ :-

⚚Area of the path

Sᴏʟᴜᴛɪᴏɴ:-

For outer circle

we, know that

circumference of circle,

where,

• Circumference of outer circle = 508m
• π = 22/7

So,

• area of circle=πr².

where,

• Circumference of inner circle = 420m

So,

➙Area of path = Area of outer circle - Area of Inner Circle

▶20518.6m² - 14032.58m²

▶6486.02m²

Hence, Area of the path is 6486.02m²