Volume and Surface Area Questions

• Three solid spheres have their radii r1, r2 and r3. The spheres are melted to form a solid sphere of bigger radius. Then the radius of the new sphere is
• The amount of extension in a spring is proportional to the weight hung on it. If the weight of 5 kgs produces an extension of 0.4 cm, what weight would produce an extension of 5cm?
• If an interior of a regular polygon is 170o, then the number of sides of the polygon is
• If PA and PB are tangents to the circle with centre O such that ∠APB=50° , then the ∠OAB=
• The length of two parallel sides of a trapezium are 18 m and 24 m. If its height is 12 m, then what is the area (in sq.m) of the trapezium?
• PQRS is a cyclic quadrilateral and PQ is the diameter of the circle. If ∠RPQ = 38°, then what is the value (in degrees) of ∠PSR?
• Smaller diagonal of a rhombus is equal to length of its sides. If length of each side is 6 cm, then what is the area (in sq.cm) of an equilateral triangle whose side is equal to the bigger diagonal of the rhombus?
• A solid cone of height 24 cm and radius of its base 8 cm is melted to form a solid cylinder of radius 6 cm and height 6 cm. In the whole process what percent of material is wasted?
• In triangle ABC, ∠ABC = 90°. BP is drawn perpendicular to AC. If ∠BAP = 50°, then what is the value (in degrees) of ∠PBC?
• In triangle PQR, the sides PQ and PR are produced to A and B respectively. The bisectors of ∠AQR and ∠BRQ intersect at point O. If ∠QOR = 50°, then what is the value (in degrees) of ∠QPR?
• If the diameter of a hemisphere is 21 cm, then what is the volume (in cub.cm) of hemisphere?
• In ΔABC, AD is the median and AD = (1/2)BC. If ∠ACD = 40°, then what is the value (in degrees) of ∠DAB?
• Circum center of ΔABC is O. If ∡BAC = 75 and ∡BCA = 80 degrees, then what is the value of ∡OAC(in deg)?
• The ratio of the volume of two cylinders is 7 : 3 and the ratio of their heights is 7 : 9. If the area of the base of the second cylinder is 154 sq. cm, then what will be the radius (in cm) of the first cylinder?
• In triangle ABC, AD, BE and CF are the medians intersecting at point G and area of triangle ABC is 156 sq.cm. What is the area (in sq.cm) of triangle FGE?
• The length of diagonal of a square is 9√2 cm. The square is reshaped to form a triangle. What is the area (in sq.cm) of largest in circle that can be formed in that triangle?
• If the radius of the cylinder is increased by 25%, then by how much percent the height must be reduced, so that the volume of the cylinder remains same?
• In ΔABC, ∠BAC = 90° and AD is drawn perpendicular to BC. If BD = 7 cm and CD = 28 cm, then what is the length (in cm) of AD?
• A chord of length 60 cm is at a distance of 16 cm from the centre of a circle. What is the radius (in cm) of the circle?
• T is a point on the common tangents at P of two circles and if TA and TB are resectively the other tangents at A and B to the two circles drawn from the point T then