The area of four walls of a room is 120 \( m^{2} \). The length of the room is twice its breadth. If the height of the room is 4 m, what is area of the floor?
The ratio of the curved surface area to the total surface area of a right circular cylinder is 1 : 2. If the total surface area is 616 \( cm^{2} \), what is the volume of the cylinder?
Into a conical tent of radius 8.4 m and vertical height 3.5 m, how many full bags of wheat can be emptied, if space required for the wheat in each bag is 1.96 \( m^{3} \)?
Let ABC be a right angled triangle with BC = 5 cm and AC = 12 cm. Let D be a point on the hypotenuse AB such that \( \angle BCD = 30^{\circ} \). What is length of CD?
Two circles touch externally and sum of their areas is \( 130\pi \) \( cm^{2} \) and the distance between their centres is 14 cm. What is the difference in the radii of the circles?
In a circle of radius 3 units, a diameter AB intersects a chord of length 2 units perpendicularly at P. If AP > BP, then what is the ratio of AP to BP?
A building is in the form of a cylinder surmounted by a hemispherical dome on the diameter of the cylinder. The height of the building is three times the radius of the base of the cylinder. The building contains \( 67\frac{1}{21} \) \( m^{3} \) of air. What is the height of the building?
