From a circular metal plate of radius 7 cm and thickness 0.16 mm, a sector is cut off containing an angle 150°. The remaining piece is moulded into a spherical bead of radius r. What is the value of r in cm?

Explanation

Remaining sector angle is 360^{\circ} - 150^{\circ} = 210^{\circ}. Volume of the remaining piece = (210/360) \times \pi \times 7^2 \times 0.016 cm = \frac{7}{12} \times 49\pi \times \frac{16}{1000} = \frac{343\pi}{750}. Setting this equal to the volume of the sphere \frac{4}{3}\pi r^3, we get r^3 = \frac{343}{1000}, so r = 0.7 cm.

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...