In the diagram, the circle has centre O and square OPQR has vertex Q on the circle. If the areaof the circle is72 sq. units , the area of the square is
Question
In the diagram, the circle has centre O and square OPQR has vertex Q on the circle. If the area of the circle is 72 sq. units, the area of the square is
Solution
The area of a circle is given by the formula πr², where r is the radius of the circle. Given that the area of the circle is 72π square units, we can set up the equation:
πr² = 72π
Dividing both sides by π, we get:
r² = 72
Taking the square root of both sides, we find that the radius r is √72 units.
In the given diagram, the radius of the circle is also the side length of the square OPQR. Therefore, the area of the square is given by the formula s², where s is the side length of the square.
Substituting √72 for s, we get:
Area of square = (√72)² = 72 square units.
So, the area of the square OPQR is 72 square units.
Similar Questions
In△PQRthe midpoints ofPQandPRareOandS respectively. If the area of OQRSis 54cm2 , find the area of △PQR .Please give 1 answer.54 cm2 36 cm2 48 cm2 72 cm2
The diagram below is formed by 4 identical circles and a square. Each circle has a radius of 14 m. What is the area of the unshaded part? Take π as 3.14.
The given figure shows two congruent circles with centres O and P respectively.Given that OP = 17 cm and OM = 15 cm, calculate the length of QR (in cm).
In the diagram, PQ and QR are tangents to the circle with centre O, at P and R respectively. Find the measure of x.
In the diagram, P QR is a line segment, ∠P QS = 125◦,∠QSR = x◦, and SQ = SR. What is the value of x?(A) 60 (B) 70 (C) 80(D) 110 (E) 125
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.