Question

find the diameter of the circle whose area is 346.5 cm square​

Answer 1

Answer:

21 cm.

Step-by-step explanation:

Area =346.5cm²

Diameter=?

Area of a circle = πr².

πr² = 346.5cm²

22/7×r² = 346.5cm²

r² = 346.5cm²×7/22

r² = 110.25

r = 10.5cm

Diameter = 2r

=2×10.5

=21cm.

Hence verified.

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Answer 2

★GIVEN★

Area of circle is 346.5 sq. cm.

★To Find★

Diameter of the circle.

★SOLUTION★

We know that area of circle is,

$\large{\pink{\underline{\boxed{\bf{Area\:of\:circle\:=\pi\:{r}^{2}}}}}}$

where,

• r is the radius
• π is 22/7 or 3.14

According to the question,

$\large\implies{\sf{Area=\pi\:{r}^{2}}}$

$\large\implies{\sf{346.5=\dfrac{22}{7}\times\:{r}^{2}}}$

$\large\implies{\sf{\dfrac{346.5\times7}{22}={r}^{2}}}$

$\large\implies{\sf{\dfrac{2425.5}{22}={r}^{2}}}$

$\large\implies{\sf{110.25={r}^{2}}}$

By square rooting both the sides,

$\large\implies{\sf{\sqrt{110.25}=r}}$

$\large\implies{\sf{\frac{+}{-}10.5=r}}$

$\large\therefore\boxed{\bf{Radius=\frac{+}{-}10.5\:cm.}}$

We know that,

$\large{\pink{\underline{\boxed{\bf{Diameter=2\times\:Radius}}}}}$

$\large\implies{\sf{d=2\times10.5}}$

$\large\therefore\boxed{\bf{Diameter=21\:cm}}$

The diameter of the circle is 21 cm.