Question

The area of circle is 154 m² where radius is 7m

true or false​

Answer 1

Given :-

• Area of the circle = 154m²

Aim :-

• To find if the radius of the circle is 7m

Formula to use :-

$\longrightarrow \sf Area\:of\:a\:circle = \pi \times (radius)^{2}$

Answer :-

Substituting the values, we get :-

• Let us assume the radius to be r.

$\implies \sf 154=\pi\times r^{2}$

Taking $\pi$ as $\sf \dfrac{22}{7}$,

$\implies \sf 154 = \dfrac{22}{7} \times r^{2}$

Transposing $\sf \dfrac{22}{7}$ to the LHS (Left hand side of the equation),

$\implies \sf 157 \div \dfrac{22}{7} = r^{2}$

$\implies \sf 154 \times \dfrac{7}{22} = r^{2}$

Reducing to the lowest terms as 22 divides 154,

$\implies \sf 7\times 7 = r^{2}$

$\implies \sf 7^{2} = r^{2}$

Cancelling the powers,

$\implies \sf (+7)\: or (-7)= r$

But since we know that the radius of the circle cannot be in negative, The radius is 7m

Hence, the radius of the circle is 7m.

Verification :-

Let us verify the answer by substituting r as 7m.

LHS (Left hand side of the equation) :-

⇒ 154m²

RHS (Right hand side of the equation) :-

⇒ π × 7²

Taking $\pi$ as $\sf \dfrac{22}{7}$

$\implies \sf \dfrac{22}{7} \times 7 \times 7$

Reducing to the lowest terms,

$\implies \sf 22\times 7$

Multiplying,

$\implies \sf 154m^{2}$

∴ LHS = RHS

Hence verified.

Some more formulas :-

• $\boxed {\sf \longrightarrow Perimeter\:of\:a\:circle = 2\times \pi \times radius}$

• Area of a triangle = ½ × base × height
• Area of a square = side × side → (side)²
• Area of rectangle = length × breadth
• Area of a parallelogram = base × height
• Area of a rhombus = ½ × Diagonal 1 × Diagonal 2