Volume and Surface Area Questions

• What part of the volume of a cube is the pyramid whose base is the base of then cube and whose vertex is the center of the cube?
• The surface areas of three faces of a cuboid sharing a vertex are 20, 32 and 40 sq. mts. What is the volume of the cuboid in cub. m?
• The two sides holding the right-angle in a right-angled triangle are 3 cm and 4 cm long. The area of its circumcircle will be in sq.cm:
• The diameters of two cylinders are in the ratio 3:2 and their volumes are equal. The ratio of their heights is
• In a quadrilateral PQRS, l_S= 90°. A circle (o, r) touches the sides PQ, QR, RS and SP at A, B, C and D respectively. If QR= 38 cm, RS = 25 cm and QA = 27 cm, find 'r'.
• The least number of square tiles of side 41 cms required to pave the ceiling of a room of size 15m 17cm long and 9m 2 cm broad is:
• O is the circumcentre of ΔABC. If AO = 8 cm, then the length of BO is
• ABCD is a quadrilateral in which BD and AC are diagonals then
• If O is the centre of a circle of radius 5 cm. At a distance of 13 cm from O, a point P is taken. From this point, two tangents PQ and PR are drawn to the circle. Then , the area of quadrilateral PQOR is
• 40 men took a dip in a pool 30 m long and 25 m broad. If the average water displaced by a man is 5 cub.m, then what will be the rise (in cm) in level of the pool?
• The length, breadth and height of a cuboid are in the ratio 19 : 11 : 13. If length is 30 cm more than height, then what is the volume (in cub.cm) of this cuboid?
• G and AD are respectively the centroid and median of the triangle ΔABC.The ratio AG:AD is
• A point P lying inside a triangle is equidistant from the vertices of the triangle. Then the triangle has P as its
• Two equal circles of radius 3 cm each and distance between their centres is 10 cm. The length of one of their transverse common tangent is
• A sphere has the same curved surface area as a cone of vertical height 40 cm and radius 30 cm. The radius of the sphere is
• Three solid spheres of radius 3 cm, 4 cm and 5 cm are melted and recasted into a solid sphere. What will be the percentage decrease in the surface area?
• In triangle ABC, a line is drawn from the vertex A to a point D on BC. If BC = 9 cm and DC = 3 cm, then what is the ratio of the areas of triangle ABD and triangle ADC respectively?
• PQR is a right angled triangle in which ∠R = 90°. If RS ⊥ PQ, PR = 3 cm and RQ = 4 cm, then what is the value of RS (in cm)?
• In triangle PQR, A is the point of intersection of all the altitudes and B is the point of intersection of all the angle bisectors of the triangle. If ∠PBR =105°, then what is the value of ∠PAR (in degrees)?
• If there are four lines in a plane, then what cannot be the number of points of intersection of these lines?