Question

Find the area of the smallest square that can be circumscribe a circle of area 154cm2

Answer 1

Answer:

98 cm²

Step-by-step explanation:

Area of circle= πr²=154 cm²

⇒   r²=154/π

⇒ r²= 154×7/22

⇒ r²= 49

⇒ r= 7 cm

diameter of circle= 2×r= 7×2= 14 cm

Diameter of circle is diagonal of square  circumscribed  =14 cm

Let a be the side of square

then, √2 a= 14

a= 14/√2

a=7√2

side of square is = 7√2 cm

area of square= a²=(7√2)²

= 49×2= 98 cm²

Answer 2

Area of circle = 154 cm²

we know, area of circle of radius R is given by,
A = πR²

so, πR² = 154

or, 22/7 × R² = 154

or, R² = 154 × 7/22 = 7 × 7

hence, R = 7 cm

we have to find area of smallest square that can be circumscribed the given circle.

so, diagonal of square = diameter of circle

√2 × side length of square = 2 × R

side length of square = 2 × 7/√2 = 7√2 cm

hence , area of square = (7√2)² = 98cm²