Question

circle and square have the same perimeter then which has the larger area​

Answer 1

Answer:

Circle

Step-by-step explanation:

Let the radius of the circle be 'R' and length of side of the square be 'x'.

 Since they have same perimeter,

⇒ perimeter of square = circumference of circle

⇒ 4side = 2πr

⇒ 4x = 2πR

⇒ x = 2πR/4

⇒ x = πR/2

⇒ x = (3.14)R/2            [π = 3.14]

⇒ x = 1.57 R

   hence,

Area of square = side² = x² = (1.57R)²

                         = 2.46 R²

Area of circle = πR² = (3.14)R²

                     = 3.14 R²

Notice that 3.14 > 2.46, which means, area of circle is greater than that of  square.

Answer 2

${\large{\pmb{\sf{\underline{Given \; that}}}}}$

★ A circle and a square have the same perimeter.

${\large{\pmb{\sf{\underline{To \; find}}}}}$

★ Which shape(circle or square have larger area).

${\large{\pmb{\sf{\underline{Solution}}}}}$

★ Circle have larger area.

${\large{\pmb{\sf{\underline{Using \; concepts}}}}}$

★ Formula to find perimeter of circle.

★ Formula to find perimeter of square.

★ Formula to find area of circle.

★ Formula to find area of square

${\large{\pmb{\sf{\underline{Using \; formulas}}}}}$

${\small{\underline{\boxed{\sf{\rightarrow Perimeter \: or \: circumference \: of \: circle \: = 2 \pi r}}}}}$

${\small{\underline{\boxed{\sf{\rightarrow Perimeter \: of \: square \: = 4 \times a}}}}}$

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

${\small{\underline{\boxed{\sf{\rightarrow Area \: of \: square \: = a \times a}}}}}$

${\large{\pmb{\sf{\underline{Where,}}}}}$

★ pi is pronounced as pi

★ The value of π is 22/7 or 3.14

★ r denotes radius

★ a denotes side of square

★ ² denotes square

${\large{\pmb{\sf{\underline{Full \; Solution}}}}}$

~ As it's given that circle and square have the same perimeter. Henceforth,

➝ 4a = 2πr

➝ a = 2πr/4

➝ a = πr/2

➝ a = 22/7r/2

➝ a = 1.57 (approx)

• Henceforth, 1.57 is the perimeter of the circle and the square.

~ Now as it's given that we have to find the larger area.

For circle -

➝ Area of circle = πr²

➝ Area of circle = 22/7r²

➝ Area of circle = 3.14r²

For square -

➝ Area of square = a×a

➝ Area of square = (1.57 × 1.57)r²

➝ Area of square = 2.46r²

• Henceforth, 3.14 < 2.46, therefore circle has more area that square.

${\large{\pmb{\sf{\underline{Additional \; information}}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto CSA \: of \: sphere \: = \: 2 \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto SA \: of \: sphere \: = \: 4 \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto TSA \: of \: sphere \: = \: 3 \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Diameter \: of \: circle \: = \: 2r}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Radius \: of \: circle \: = \: \dfrac{d}{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Volume \: of \: sphere \: = \: \dfrac{4}{3} \pi r^{3}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Area \: of \: circle = \: \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Circumference \: of \: circle \: = \: 2 \pi r}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Diameter \: of \: circle \: = \: 2r}}}$