Surface Area and Volume Quiz

Q1: A cylindrical pencil sharpened at one edge is the combination of

Q2: If the surface areas of two spheres are in ratio 16 : 9, then their volumes will be in the ratio:

Q3: The lateral surface area of a right circular cone of height 28 cm and base radius 21 cm(in sq. cm) is:

Q4: A cylindrical pencil sharpened at one edge is the combination of

Q5: The base area of the cylinder is 80 sq.cm. If its height is 5cm, then its volume is

Q6: A cylinder and a cone are of the same base radius and same height. Find the ratio of the volumes of the cylinder of that of the cone.

Q7: A cone is cut through a plane parallel to its base and then the cone that is for medon one side of that plane is removed. The new part that is left over on the other side of the plane is called

Q8: A cylinder, a cone and a hemisphere are of equal base and have the same height. What is the ratio of their volumes?

Q9: If the ratio of the radius of a cone and a cylinder of equal volume is 3:5, then find the ratio of their heights.

Q10: A shuttlecock used for playing badminton has the shape of the combination of

Q11: A bucket of height 12 cm, has a top and bottom diameter of 40 cm and 20 cm respectively. The cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per dm2 will be​

Q12: A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.

Q13: During conversion of a solid from one shape to another, the volume of the new shape will

Q14: If the area of three adjacent faces of cuboid are X, Y and Z respectively, then the volume of cuboid is:

Q15: An iron rod of diameter 1cm and length 8cm is drawn into a wire of length 18m of uniform thickness. Find the thickness of the wire?

Q16: The slant height of the frustum of a cone having radii of two ends as 5 cm and 2 cm respectively and height 4 cm is

Q17: If the volume of a cube is 343 cm , then its edge is

Q18: What is the area of a semi–circle of radius 5 cm?

Q19: A right circular cylinder of radius r cm and height h cm (h>2r) just encloses a sphere of diameter

Q20: The volumes of two spheres are in the ratio 27 : 8. The ratio of their curved surface is:

Q21: What do you understand by the quantity called ‘area’?

Q22: The total surface area of a hemispherical solid having radius 7 cm is

Q23: The radii of the circular ends of a conical curd container, 6 cm high are 16 cm and 24 cm. The volume of the container in litres will be​

Q24: A hollow cube of internal edge 22cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that 1/8th space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is

Q25: The ratio of the volumes of two spheres is 8 : 27. If r and R are the radii of spheres respectively, then (R – r): r is:

Q26: A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, of diameter 3.5 cm and height 3cm. The number of cones so formed is:

Q27: A solid formed on revolving a right angled triangle about its height is

Q28: An open container made up of a metal sheet is in the form of a frustum of a cone of height 8 cm with radii of its lower and upper ends as 4 cm and 10 cm respectively. The cost of the oil at the rate of Rs. 50 per litre, which can completely fill the container, will be

Q29: A metallic spherical shell of internal and external diameters 4 cm and 8 cm respectively, is melted and recast into the form of a cone with base diameter 8cm. The height of the cone is

Q30: The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their volumes is:

Q31: How many dimensions are required to make a cuboid?

Q32: The surface area of a sphere is 616 cm2. Its radius is

Q33: The ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube is

Q34: A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is

Q35: If the radius of base of a right circular cylinder is halved, keeping the height same, the ratio of the volume of the reduced cylinder to that of the original cylinder is:

Q36: There are 2 identical cubes each having a total surface area equal to ‘A’. Let ‘S’ be the surface area of the solid obtained by joining these 2 cubes end to end. Which of the following statements is true?

Q37: If a solid right circular cone of height 24 cm and base radius 6 cm is melted and recast in the shape of a sphere, then the radius of the sphere is​

Q38: If two solid hemispheres of same base radii r, are joined together along their bases, then curved surface area of this new solid is

Q39: If the volumes of a cube is 1728 cm³, the length of its edge is equal to:

Q40: A piece of cloth is required to completely cover a solid object. The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7 m and height of the cone is 1 m, what is the area of cloth required?

Q41: A cylinder and a cone are of same base radius and of same height. The ratio of the volume of the cylinder to that of the cone is

Q42: If two solid hemispheres of same base radius ‘x’ cm are joined together along their bases, then the CSA of the new solid formed is

Q43: 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

Q44: The volume (in cm³) of the largest right circular cone that can be cut off from a cube of edge 4.2 cm is: .

Q45: Ram has a semicircular disc. He rotates it about its diameter by 360 degrees. When he rotates the disc, a volume of air in his room gets swept. What is the name of the object/shape that exactly occupies this volume?

Q46: The volume of a sphere is 4851 cm3. Its diameter is

Q47: The largest possible sphere is carved out from a cube of 7 cm side. The volume of the sphere will be

Q48: 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

Q49: The circumference of the edge of hemispherical bowl is 132 cm. When π is taken as 22/7, the capacity of bowl in cm³ is:

Q50: A bucket is in the form of a frustum of a cone, its depth is 15 cm and the diameters of the top and the bottom are 56 cm and 42 cm respectively. How many liters of water can the bucket hold?

Q51: A piece of paper is in the shape of a semi¬circular region of radius 10 cm. It is rolled to form a right circular cone. The slant height is

Q52: A cubical block of side 7 cm is surmounted by a hemisphere. The greatest diameter of the hemisphere is

Q53: 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

Q54: The surface areas of two spheres are in the ratio 1 : 2. The ratio of their volume is:

Q55: A 20 m deep well of diameter 7 m is dug and the earth taken out is evenly spread out to form a platform of 22 m by 14 m. Find the height of the platform (in m).

Q56: The base radii of two circular cones of the same height are in the ratio 3 : 5. The ratio of their volumes are

Q57: A container (open at the top) made up of metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends 8cm and 20 cm respectively. The amount of liquid the container can hold is (Take π = 3.14) ​

Q58: The diameters of the two circular ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35 cm. The capacity of the bucket is

Q59: The radius of spherical balloon increases from 8 cm to 12 cm. The ratio of the surface areas of balloon in two cases is:

Q60: A cylindrical tank is filled by pumping water from a cuboidal tank of dimensions 200cm × 150cm × 95 cm. The radius of the cylindrical tank is 60cm and height is 95cm. Find the height (in m) of the water left in the cuboidal tank after the cylindrical tank is completely filled. (Take π = 3.14)