Volume and Surface Area Questions

• Points P and Q lie on side AB and AC of triangle ABC respectively such that segment PQ is parallel to side BC. If the ratio of AP:PB is 1:4 and area of Δ APQ is 4 sq cm, what is the area of trapezium PQCB?
• In ΔDEF, G and H are points on side DE and DF respectively. GH is parallel to EF. If G divides DE in the ratio 3:2 and HF is 8 cm, then the length of DF is
• The total surface area of a hemisphere is 462 sq cm, what is its curved surface area? (Take π = 22/7)
• Δ DEF and Δ GHI are similar triangles. Length of AB is 10 cm and length of the corresponding side DE is 6 cm. What is the ratio of Perimeter of ΔABC to ΔDEF?
• In a cyclic quadrilateral ABCD ∠BCD=120° and passes through the centre of the circle. Then ∠ABD = ?
• The midpoints of AB and AC of a triangle ABC are X and Y respectively. If BC+XY=12 units, then BCXY is
• In an isosceles ΔABC, AD is the median to the unequal side meeting BC at D. DP is the angle disector of ∠ADB and PQ is drawn parallel to BC meeting AC at Q. Then the measure of ∠PDQ is
• An angle is smaller than its supplementary by 30°. What is the measure of the angle?
• A square is inscribed in a circle. If the side of the square is 14 cm, what is the area (in sq.cm) of the circle?
• A wooden bowl is in shape of a hollow hemisphere of internal radius 7 cm and thickness 1 cm. What is the total surface area (in sq.cm) of the bowl? (Take: = 22/7)
• A chord of length 16 cm is drawn in a circle of radius 10 cm. The distance of the chord from the centre of the circle is
• An angle in a semicircle is
• If in ΔABC, DE ||BC, AB = 7.5cm, BD = 6cm and DE = 2cm, then the length of BC in cm is
• A circle is inscribed in a square. If the length of the diagonal of the square is 14√2 cm, what is the area (in sq cm) of the circle?
• A cone of radius 7 cm and height 12 cm is completely filled with water. This water is emptied into an empty cylindrical vessel of radius 3.5 cm. What will be the height of water in this vessel?
• The total surface area of a hemisphere is 166.32 sq cm, find its radius?
• ΔABC is similar to ΔDEF. Length of AB is 18 cm and length of the corresponding side DE is 10 cm. What is the ratio of Perimeter of ΔABC : Perimeter of ΔDEF?
• Volume of a cylinder is 770 cubic cm. If circumference of its base is 22 cm, what will be the curved surface area of the cylinder? (Take π = 22/7)
• What will be the sum of the measures all the interior angles of a polygon having 14 sides?
• In a triangle the length of the side opposite the angle which measures 45° is 8 cm, what is the length of the side opposite to the angle which measures 90°?