Volume and Surface Area Questions

• The lengths of two diagonals of a rhombus are 24 cm and 32 cm. What is the side (in cm) of the rhombus?
• PQRS is a square, M is the mid-point of PQ and N is a point on QR such that NR is two-third of QR. If the area of ΔMQN is 48 cm2 , then what is the length (in cm) of PR ?
• The tangents drawn at points A and B of a circle with centre O, meet at P. If ∠AOB = 120° and AP = 6 cm, then what is the area of triangle (in cm2) APB?
• Due to increase of k% in the side, the area of a square increases by 69%. What is the value of k?
• The length of diagonal BD of a parallelogram ABCD is 36 cm. P and Q are the centroids of triangle ABC and triangle ADC respectively. What is the length (in cm) of PQ?
• If an equilateral triangle has side 12 cm, then what is the difference (in cm) between the circumradius and inradius?
• The lengths of two parallel sides of a trapezium are 21 cm and 9 cm. If its height is 10 cm, then what is the area (in cm2) of the trapezium?
• In triangle ABC, ∠ABC = 90°. BP is drawn perpendicular to AC. If ∠BAP = 30°, then what is the value (in degrees) of ∠PBC?
• A solid cone of height 36 cm and radius of base 9 cm is melted to form a solid cylinder of radius 9 cm and height 9 cm. What percent of material is wasted this process?
• Diameter of wheel of a cycle is 21 cm. The cyclist takes 45 minutes to reach a destination at a speed of 16.5 km/hr. How many revolutions will the wheel make during the journey?
• The side BC of ΔABC is produced to D. If ∠ACD = 114° and ∠ABC= (1/2)∠BAC, then what is the value (in degrees) of ∠BAC?
• O is the center of the circle and two tangents are drawn from a point P to this circle at points A and B. If ∠AOP = 50°, then what is the value (in degrees) of ∠APB?
• In ΔPQR, PQ = PR = 18 cm, AB and AC are parallel to lines PR and PQ respectively. If A is the mid-point of QR, then what is the perimeter (in cm) of quadrilateral ABPC?
• In ΔPQR, PS and PT are bisectors of ∠QPR and ∠QPS respectively. If ∠QPT = 30°, PT = 9 cm and TR = 15 cm, then what is the area (in cm2) of ΔPTR
• How many spherical balls of radius 1 cm can be made by melting a hemisphere of radius 6 cm?
• The point of intersection of all the angle bisector of a triangle is ______ of the triangle.
• ABC is an equilateral triangle and P is the orthocenter of the triangle, then what is the value (in degrees) of ∠BPC?
• In a triangle ABC, AD is angle bisector of ∠A and AB : AC = 3 : 4. If the area of triangle ABC is 350 cm2, then what is the area (in cm2) of triangle ABD?
• If the radius of the cylinder is decreased by 20%, then by how much percent the height must be increased, so that the volume of the cylinder remains same?
• ΔPQR has sides PQ and PR measuring 983 and 893 units respectively. How many such triangles are possible with all integral sides?