What is the area of the shaded region?
Consider the following for the next three (03) items that follow:<br>Two circles with centres at O_{1} and O_{2} touching each other are placed inside a rectangle of sides 9 cm and 8 cm as shown in the figure given below.
- A. \frac{240-10\pi-\pi\theta}{24} square unit
- B. \frac{240-6\pi-\pi\theta}{24} square unit
- C. \frac{120-12\pi-\pi\theta}{24} square unit
- D. \frac{240-12\pi-\pi\theta}{24} square unit ✓
Correct Answer: D. \frac{240-12\pi-\pi\theta}{24} square unit
Explanation
The shaded area is found by subtracting the respective circular sectors and bounding unshaded geometric fragments from the total area of the rectangle. Evaluating the geometric constraints gives the explicit area formula \frac{240-12\pi-\pi\theta}{24} square units.
Related questions on Mensuration
- A pendulum swings through an angle of 30° and its end describes an arc of length 55 cm. What is the length of the pendulum? (Take $\pi = 22/...
- A conical tent has an angle of 60° at the vertex. If the curved surface area is 100 m^2, then what is the volume of the tent?
- A right circular cone and a hemisphere have equal base and equal volume. What is the ratio of the height of the cone to the radius of the he...
- A wire is in the form of an equilateral triangle with an area of 36\sqrt{3} cm^2. If it is changed into a semicircle, then what is its r...
- Let the area of the largest possible square inscribed in a circle of unit radius be x. Let the area of the largest possible circle inscribed...