Question
PQRS is a cyclic trapezium where PQ is parallel to RS
and PQ is the diameter. If ∠QPR = 40° then the ∠PSR is equal to:Solution
Angle made in a semicircle is a right angle. The sum of the opposite angles of a cyclic trapezium is 180°. In triangle PQR, ∠RPQ + ∠RQP + ∠QRP = 180° [Angle sum property] ⇒ 40° + ∠RQP + 90° = 180° ⇒ ∠RQP = 180° - 130° = 50° ∠RQP + ∠PSR = 180° [Supplementary Angles] ∴ ∠PSR = 180° - 50° = 130°
A rectangular field is 35 m long and 24 m wide. Find the cost of levelling it at Rs. 8 per square metre.
Find the time taken by a pipe, which releases 94.5 m3 of water in a minute to fill an empty cylindrical tank of radius 12 m and height 14 m. ...
Nine cubes with each side measuring 3 cm are aligned in a straight row to build a cuboid. What is the total surface area of the resulting cuboid?
The length is increased by 25%, breadth remains unchanged, and the height is reduced by 20%. Find the net percentage change in volume.
The perimeter of a square field is 16 cm more than the perimeter of a rectangle. The length of the rectangle is 72 cm which is 300% of its width. If a s...
1.5 cm of rain has fallen on a square km of length 80% of the water was stored in a tank of dimensions 160 m × 15m. Find the increase in the water leve...
Three metallic cubes whose sides are 15 cm, 20 cm and 25 cm respectively are melted and converted into a single cube. If there is no loss of metal in t...
The sum of the perimeters of a square and a rectangle is 120 metres. If the sum of the length and breadth of the rectangle is 30 m, then find the area o...
A maximum size sphere is cut from a hemisphere of radius r. Find the ratio of volume of hemisphere to sphere?
A cone and a cylinder have the same radius and height. If the volume of the cone is 100 cm³, what is the volume of the cylinder?
Relevant for Exams:
