mrk9414 wrote:
Carcass wrote:
The circumference of a circle is \(\frac{
7}{8}\) the perimeter of a square.
Quantity A |
Quantity B |
The area of the square |
The area of the circle |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
can someone please explain it ... I didn't get above-mentioned solution
thanks in advance for your kindness
Let the radius of circle be \(r\) and side of square be \(a\)
Given \(2πr = \frac{7}{8}(4a)\)
i.e. \(\frac{2πr(8)}{7(4)} = a\)
\(a = \frac{4πr}{7}\)
Now,
Col. A: \(a^2\)
Col. B: \(πr^2\)
Put the value of \(a\) in Col. A;
Col. A: \((\frac{4πr}{7})^2\)
Col. B: \(πr^2\)
Col. A: \(\frac{16π^2r^2}{49}\)
Col. B: \(πr^2\)
Dividing both sides by \(πr^2\);
Col. A: \(\frac{16π}{49}\)
Col. B: \(1\)
Multiplying both sides by \(49\);
Col. A: \(16π\)
Col. B: \(49\)
Put \(π = 3.14\),
Col. A: \(50.24\)
Col. B: \(49\)
Hence, option A