Question

Please tell me question no. 8 with solutions (with attachment) Please tell me fast​

Answer 1

Questions

(i) A circular pond of diameter 28 m is surrounded by a path 7 m wide. Find the area of the path.

(ii) Find the area of a 2 m wide circular path surrounding a circular plot of radius 20 m.

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Answers

(i)

Given

• The diameter of circular pond is 28 m
• The pond is surrounded by a path 7 m wide

To Find

• The Area of the Path

Solution

Area of Path ⇒ Area of the Pond with Path - Area of the Pond

Radius of Pond ⇒ $\dfrac{28}{2} + 7$ = 21 m

Radius of Pond along with Path ⇒ 27 - 7 = 14 m

Area of Path ⇒ π (R² - r²)

⇒ π {(21)² - (14)²}

⇒ $\dfrac{22}{7} \{ 441 - 196\}$

⇒ $\dfrac{22}{7} \times 245$

⇒ $\dfrac{22}{7\div 7} \times 245\div 7$

⇒ $22 \times 35$

⇒ 770 m²

∴ The area of the path is 770 m²

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(ii)

Given

• The radius of the circular plot is 20 m
• The circular plot is surrounded with a 2 m wide circular path.

To Find

• The Area of the Path

Solution

Area of Path ⇒ Area of the Plot with Path - Area of the Plot

Radius of Plot ⇒ 20 + 2 = 22 m

Radius of Plot along with Path ⇒ 22 - 2 = 20 m

Area of Path ⇒ π (R² - r²)

⇒ π {(22)² - (20)²}

⇒ $\dfrac{22}{7} \{ 484 - 400\}$

⇒ $\dfrac{22}{7} \times 84$

⇒ $\dfrac{22}{7\div 7 } \times 84\div 7$

⇒ $22\times 12$

⇒ 264 m²

∴ The area of the path is 264 m²

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Answer 2

Answer:

$\huge { \boxed{ \underline{ \sf{ \orange{Question?}}}}}$

• (i) A circular pond of diameter 28 m is surrounded by a path 7 m wide. Find the area of the path.

• (ii) Find the area of a 2 m wide circular path surrounding a circular plot of radius 20 m.

$\huge { \boxed{ \underline{ \sf{ \purple{Answer:- }}}}}$

(i) A circular pond of diameter 28m is surrounded by a path 7m wide. Find the area of the path.

$\huge { \boxed{ \underline{ \sf{ \green{Given:- }}}}}$

• Diameter of a circular pond = 28 m

• Path wide = 7 m

$\huge { \boxed{ \underline{ \sf{ \pink{To find:- }}}}}$

• Area of the path

$\huge { \boxed{ \underline{ \sf{ \purple{Solution:- }}}}}$

$\\ \\ \: \: \: \: \: Area \: of \: the \: path \: = \pi(R {}^{2} - r {}^{2} ) \\ \\ \\ R = \frac{28}{2} + 7 \\ \\ = 14 + 7 \\ \\ = 21 \: m \\ \\ \\ \\ r = 21 - 7 = 14m$

$\\ \\ Area \: of \: the \: path \: = \pi( {21}^{2} - {14}^{2} ) \\ \\ = \frac{22}{7} \times 245 \\ \\ = 770m {}^{2}$

(ii) Find the area of a 2 m wide circular path surrounding a circular plot of radius 20 m.

$\huge { \boxed{ \underline{ \sf{ \green{Given:- }}}}}$

• Radius of a circular plot = 20 m

• Circular path wide = 2 m

$\huge { \boxed{ \underline{ \sf{ \pink{To find:- }}}}}$

• Area of the path

$\huge { \boxed{ \underline{ \sf{ \purple{Solution:- }}}}}$

$\\ \\ Area \: of \: the \: circular \: path \: = \pi( {R}^{2} - {r}^{2} ) \\ \\ R = 20 + 2 \\ \\ = 22 \\ \\ \\ r = 22 - 2 \\ \\ = 20m \\ \\ \\ Area \: of \: the \: circular \: path = \pi( {22}^{2} - {20}^{2} ) \\ \\ = \frac{22}{7} \times 84 \\ \\ = 264m {}^{2}$