Practice Test

Q1) A cylindrical pencil sharpened at one edge is the combination of Show Answer

Q2) A surahi is the combination of Show Answer

Q3) A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that 1/8 space of the cube remains unfilled. Then, the number of marbles that the cube can accommodate is Show Answer

Q4) A medicine-capsule is in the shape of a cylinder of diameter 0.5 cm with two hemispheres stuck to each of its ends. The length of entire capsule is 2 cm. The capacity of the capsule is Show Answer

Q5) If two solid hemispheres of the same base radius ‘r’ are joined together along their bases, then curved surface area of this new solid is Show Answer

Q6) A right circular cylinder of radius r cm and height h cm (where, h > 2r) just encloses a sphere of diameter Show Answer

Q7) A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form a cone of base diameter 8 cm. The height of the cone is Show Answer

Q8) A solid piece of iron in the form of a cuboid of dimensions 49 cm x 33 cm x 24 cm, is moulded to form a solid sphere. Then, radius of the sphere is Show Answer

Q9) Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is Show Answer

Q10) During conversion of a solid from one shape to another, the volume of the new shape will Show Answer

Q11) The number of solid spheres, each of diameter 6 cm that can be made by melting a solid metal cylinder of height 45 cm and diameter 4 cm is Show Answer

Q12) Assertion (A) : In a right circular cone, the cross-section made by a plane parallel to the base is a circle.
Reason (R) : If the volume and the surface area of a solid hemisphere are numerically equal, then the diameter of hemisphere is 9 units. Show Answer

Q13) Assertion (A) : If the volume of two shperes are in the ratio 64 : 27, then the ratio of their surface areas is 4 : 3.
Reason (R) : If the surface areas of two shperes are in the ratio 16 : 9, then the ratio of their volumes is 64 : 27. Show Answer

Q14) Assertion (A) : The number of solid spheres of diameter 6 cm can be made by melting a solid metallic cylinder of height 45 cm and diameter 4 cm, is 5.
Reason (R) : If three solid metallic spherical balls of radius 3 cm, 4 cm and 5 cm are melted into a single spherical ball, then its radius is 6 cm. Show Answer

Q15) Assertion (A) : If 12 solid spheres of the same size are made by melting a solid metallic cone of base radius 1 cm and height of 48 cm, then radius of each sphere is 2 cm.
Reason (R) : If three cubes of iron whose edges are 3 cm, 4 cm and 5 cm respectively are melted and formed into a single cube, then the edge of the single cube is 6 cm. Show Answer

Q16) The volume of cylindrical cup is Show Answer

Q17) The volume of hemispherical cup is Show Answer

Q18) Which container had more juice and by how much? Show Answer

Q19) The height of the conical tent prepared to accommodate four students is Show Answer

Q20) How much space on the ground is occupied by each student in the conical
tent Show Answer

Q21) Calculate the volume of the hemispherical dome if the height of the dome is 21 m Show Answer

Q22) The formula to find the Volume of Sphere is Show Answer

Q23) The cloth require to cover the hemispherical dome if the radius of its base is 14m is Show Answer

Q24) The volume of the cuboidal shaped top is with dimensions mentioned in Show Answer

Q25) The length of the diagonal if each edge measures 6cm is Show Answer

Q26) Volume of the solid figure if the length of the edge is 7cm is Show Answer

Q27) What is the curved surface area of hemisphere (ice cream) if the base radius is 7cm? Show Answer

Q28) Slant height of a cone if the radius is 7 cm and the height is 24 cm _______ Show Answer

Q29) The total surface area of cone with hemispherical ice cream is Show Answer

Q30) What is the volume of cuboid? Show Answer

Q31) What is the volume of a conical depression? Show Answer

Q32) What is the total volume of conical depression? Show Answer

Q33) What is volume of wood in the entire stand? Show Answer

Q34) The given problem is based on which mathematical concepts? Show Answer

Q35) Three cubes each of side 5cm are joined end to end, then the surface area of the resulting solid is Show Answer

Q36) A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is Show Answer

Q37) A cubical icecream brick of edge 22 cm is to be distributed among some children by filling icecream cones of radius 2 cm and height 7 cm upto its brim. How many children will get icecream cones? Show Answer

Q38) A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is Show Answer

Q39) Two cones have their heights in the ratio 1:3 and radii in the ratio 3:1, then the ratio of their volumes is Show Answer

Q40) A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is Show Answer

Q41) The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. The length of the wire is Show Answer

Q42) From a solid circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and same base is removed, then the volume of remaining solid is Show Answer

Q43) A 20 m deep well, with diameter 7 m is dug and the the earth from digging is evently spread out to form a platform 22 m by 14 m. The height of the platform is Show Answer

Q44) If the radius of the base of a right circular cylinder is halved, keeping the height same, then find the ratio of the volume of the cylinder thus obtained to the volume of original cylinder. Show Answer

Q45) Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. The water level rises by 5.6 cm. When marble dropped into the beaker, then the number of marble is Show Answer

Q46) A heap of rice is in the form of a cone of base diameter 24 m and height 3.5m. Find the volume of the rice. How much canvas as cloth is required to just cover the heap? Show Answer

Q47) The radius of the sphere so formed is Show Answer

Q48) The volume of the sphere so formed is Show Answer

Q49) Find the ratio of the volume of sphere to the volume of cylinder Show Answer

Q50) Total surface area of the cylinder is Show Answer

Q51) During the conversion of a solid from one shape to another the volume of new shape will Show Answer

Q52) Curved surface area of the cylinder made by Geeta is Show Answer

Q53) The ratio of curved surface area of the cylinder made by Geeta and Meena is Show Answer

Q54) The volume of the cylinder made by Meena is Show Answer

Q55) The ratio of the volume of the cylinders made by Geeta and Meena is Show Answer

Q56) When two CD Cassette are shifted from Geeta cylinder to Meena's cylinder, then Show Answer

Q57) How much cubes of side 2 cm can be made from a solid cube of side 10 cm? Show Answer

Q58) A solid spherical ball fits exactly inside the cubical box of side 2a. The volume of the ball is Show Answer

Q59) A cone and a cylinder have the same radii but the height of the cone is 3 times that of the cylinder, then the ratio of their volumes. Show Answer

Q60) After craving out cone from the cylinder Show Answer

Q61) Find the slant height of the conical cavity so formed. Show Answer

Q62) The curved surface area of the conical cavity so formed is Show Answer

Q63) External curved surface area of the cylinder is Show Answer

Q64) Volume of conical cavity is Show Answer

Q65) A cube whose edge is 20 cm long, has circles on each of its faces painted black. What is the total area of the unpainted surface of the cube if the circles are of the largest possible areas? Show Answer

Q66) If two solid hemisphere of the same base radius r are joined together along their bases, then curved surface area of this new solid is Show Answer

Q67) The radius (in cm) of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is Show Answer

Q68) Given that 1 cu. cm of marble weighs of 28 cm in width of a marble block of 28 cm in width and 5 cm thick, is 112 kg. The length of the block is Show Answer

Q69) A sphere and a cube have equal surface areas. The ratio of the volume of the sphere to that of cube is Show Answer

Q70) A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then the water level rises (in cm) by Show Answer

Q71) Three cubes of iron whose edges are melted and formed into a single cube. The edge of the new cube formed is _________. Show Answer

Q72) A river 1.5 m deep and 36 m wide is flowing at the rate of 3.5 km per hour. The amount of water that runs into the sea per minute (in cubic meters) is Show Answer

Q73) The number of coins, 1.5 cm in diameter and 0.2 cm thick to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm is Show Answer

Q74) A shuttle cock for playing badminton has the shape of the combination of Show Answer

Q75) A cone is cut through a plane parallel to its base and then the cone that is formed on one side of that plane is removed. The new part that is left over on the other side of the plane is called Show Answer

Q76) In a right circular cone, the cross-section made by a plane parallel to the base is a Show Answer