Question

The total area of a circle and a square is equal to 5450 sq.cm. The diameter of the circle is 70 cm. What is the sum of the circumference of the circle and the perimeter of the square?

• A. 360 cm
• B. 380 cm
• C. Cannot be determined
• D. None of these

Answer 1

The correct option is B

380 cm

Given that, the diameter of the circle is 70 cm. Therefore radius of circle = 35 cm. Let each side of a square be x cm. Also given that the total area of the circle and the square is equal to 5450 sq.cm.

Therefore $\pi r^2+x^2=5450$

Or $\pi \times 35\times 35+x^2=5450$

Or $\frac{22}{7}\times 35\times 35+x^2=5450$

Or 22 $\times 5\times 35+x^2=5450$

Or $x^2=5450-3850=1600$

Therefore $x=40$ cm.

Now required sum = $\pi \times 2\times 35+4\times 40$

$=\frac{22}{7}\times 2\times 35+160=220+160=380$ cm.