Question

3 Multiple choice questions
(i) The area of a circle is 2464 m², then the diameter of the circle is
(a) 56 m
(b) 154 m
(c) 176 m
(d) None of these​

Answer 1

$\huge{\underline{\underline{\bf{Solution}}}}$

$\rule{200}{2}$

$\tt given\begin{cases} \sf{Area \: of \: circle \: is \: 2464 \: m^2.} \end{cases}$

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{To \: Find :}}}}$

We have to find the Diameter of the circle.

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{Explanation :}}}}$

We know that,

$\Large{\star{\boxed{\sf{Area = \pi r^2}}}}$

$\sf{\dashrightarrow Area = \frac{22}{7} \times r^2} \\ \\ \sf{\dashrightarrow \cancel{2464} \times \frac{7}{\cancel{22}} = r^2} \\ \\ \sf{\dashrightarrow 112 \times 7 = r^2} \\ \\ \sf{\dashrightarrow 784 = r^2} \\ \\ \sf{\dashrightarrow r = \sqrt{784}} \\ \\ \sf{\dashrightarrow r = 28 \: m}$

$\rule{200}{2}$

We know that,

$\Large{\star{\boxed{\sf{Diameter = 2 \times Radius}}}}$

$\sf{\dashrightarrow Diameter = 2 \times 28} \\ \\ \sf{\dashrightarrow Diameter = 56} \\ \\ \sf{\therefore \: Diameter \: of \: circle \: is \: 56 \: m.}$

Option (a) is correct.

Answer 2

Finding Diameter of the circle:

Step-by-step explanation:

$\ Given value:\\\\\ Area \ of \ circle = 2464 m^2 \\\\\ Find:\\\\Diameter=?\\\\\ Solution:\\\\\ formula: \\\\ \ area \ of \ circle = \pi \ r^2 \\\\\ Diameter \ = 2 r\\\\\ Calculate \ radius \\\\\rightarrow \ 2464 \ = \pi r^2 \\\\\rightarrow \ 2464 \ = \frac{22}{7} r^2 \\\\\rightarrow \ 2464\times \frac{7}{22} \ = r^2 \\\\\rightarrow r^2= \ 112\times 7 \\\\\rightarrow r^2= \ 784 \\\\\rightarrow r^2= \ (28)^2 \\\\ \rightarrow r= \ 28$

$\ Diameter= 2\times r\\\\\ Diameter= 2 \times 28\\\\\ Diameter= 56$

$\ Option \ a \ is \ the \ correct \ answer \ to \ this \ question$

Learn more:

• Diameter the circle: https://brainly.in/question/5636928