SURFACE AREA AND VOLUME (CLASS 10)
COMPETENCY BASED MCQ QUESTIONS
Q1.The surface area of a cube is 216 cm2 , its volume is
(a) 144 cm3 (b) 196 cm3 (c) 212 cm3 (d) 216 cm3
Q2. A solid is hemispherical at the bottom and conical above. If the surface area of the two
parts
equal, then the ratio of its radius and the height of its conical part is
(a) 1: 3 (b) 1 : √3 (c) 1 : 1 (d) √3 : 1
Q3. The radius (in cm) of the largest right circular cone that can be cut out of cube of edge
4.2
cm is
(a) 4.2 cm (b) 2.1 cm (c) 8.1 cm (d) 1.05 cm
Q4. A rectangular sheet of paper 40 cm x 22 cm, is rolled to form a hollow cylinder of height
40
cm. The radius of the cylinder (in cm) is
(a) 3.5 (b) 7 (c) 80/7 (d) 5
Q5. If two solid hemispheres of same base radius are joined together along their bases, then
curved surface area of this new solid is
(a) 3𝜋𝑟2 (b) 4𝜋𝑟2 (c) 5𝜋𝑟2 (d) 6𝜋𝑟2
Q6. The ratio of surface areas of two spheres is 9:4. The ratio of their volumes
(a)27:8 (b)8:27 (c) 3:2 (d) 2:3
Q7. The base radii of two right circular cones of the same height is 3:5. The ratio of their
columns is
(a)25:9 (b)9:25 (c) 3:5 (d) 5:3
Q8. A cone, a hemisphere and a cylinder stand on equal bases and have equal height. The
ratio of
their volumes is
(a) 1:2:3 (b)2:3:4 (c)1:3:4 (d)2:3:5
Q9. What is the volume in cu cm of a cube whose surface area is 1944 sq cm?
(a) 1728 cm3 (b)4096 cm3 (c) 2744 cm3 (d)5832 cm
Q10. The shape of an ice-cream cone is a combination of:
(a) Sphere + cylinder (b) Sphere + cone (c) Hemisphere + cylinder (d) Hemisphere + cone
Q11. If a cone is cut parallel to the base of it by a plane in two parts, then the shape of the top
of
the cone will be a:
(a) Sphere (b) Cube (c) Cone itself (d) Cylinder
Q12. If r is the radius of the sphere, then the surface area of the sphere is given by;
(a) 4 π r2 (b) 2 π r2 (c) π r2 (d) 4/3 π r2
Q13. If we change the shape of an object from a sphere to a cylinder, then the volume of
cylinder
will
(a) Increase (b) Decrease (c) Remains unchanged (d) Doubles
Q14. If a cylinder is covered by two hemispheres shaped lid of equal shape, then the total
curved
surface area of the new object will be
(a) 4πrh + 2πr2 (b) 4πrh – 2πr2 (c) 2πrh + 4πr2 (d) 2πrh + 4πr
Q15. If we join two hemispheres of same radius along their bases, then we get a;
(a) Cone (b) Cylinder (c) Sphere (d) Cuboid
Q16. A cylindrical pencil sharpened at one edge is the combination of
(a) a cone and a cylinder (b) frustum of a cone and a cylinder (c) a hemisphere and a
cylinder
(d) two cylinders
Q17. Two identical solid cubes of side a are joined end to end. Then the total surface area of
the
resulting cuboid is
(a) 12a2 (b) 10a2 (c) 8a2 (d) 11a2
Q18. A solid cylinder of radius r and height h is placed over another cylinder of same height
and
radius. The total surface area of the shape so formed is
(a) 4πrh + 4πr2 (b) 2πrh + 4πr2 (c) 2πrh + 2πr2 (d) 4πrh + 2πr2
Q19. Consider a spherical shell having external radius = R and internal radius = r. Then,
volume of the material = ___cubic units.
( a) r3 ( b) R3 ( c) (r3 + R3) ( d) none of
the above
Q20. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The
diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner
surface area of the vessel.
( a) 572 cm2 ( b) 570 cm2 ( c) 562 cm2 ( d)
569 cm2
Q21. A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest
diameter the hemisphere can have?
( a) 7 cm ( b) 12 cm ( c) 14 cm
( d) 3.5 cm
Q22. A tent is in the shape of a cylinder surmounted by a conical top. If the height and
diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top
is 2.8 m, find the area of the canvas used for making the tent. (Note that the base of the tent
will not be covered with canvas.)
( a) 40 m2 ( b) 48 m2 ( c) 42 m2 ( d) 44 m2
Q23. A tent is in the shape of a cylinder surmounted by a conical top. If the height and
diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top
is 2.8 m, find the cost of the canvas of the tent at the rate of Rs 500 per . (Note that the base
of the tent will not be covered with canvas.)
( a) Rs 20000 ( b) Rs 22000 ( c) Rs 24000 ( d) Rs
21000
Q24. A right triangle, whose sides are 3 cm and 4 cm (other than hypotenuse) is made to
revolve about its hypotenuse. Find the surface area of the double cone so formed.
( a) 52.2 cm2 ( b) 52.57 cm2 ( c) 52.75 cm2
( d) 52.55 cm2
Q25. A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5
cm and it is assumed that space of the cube remains unfilled. Then the number of marbles
that the cube can accommodate is
( a) 142296 ( b) 142396 ( c) 142496 ( d) 142596
Q26. The breadth of a room is twice its height and is half of its length. The volume of room is
512dm³ .Its dimensions are
(a) 16 dm, 8 dm, 4 dm (b) 12 dm, 8 dm, 2 dm (c) 8 dm, 4 dm, 2 dm (d) 10 dm, 15
dm, 20 dm
Q27. The slant height and base diameter of a conical tomb are 25 m and 14 m respectively.
The cost of white washing its curved surface at the rate of Rs. 210 per 100 m² is
(a) Rs. 1233 (b) Rs. 1155 (c) Rs. 1388 (d) Rs. 1432
Q28. If base radius and height of a cylinder are increased by 10% then its volume increased
by:
(a) 30% (b) 40% (c) 42% (d) 33.1%
Q29. The volume and the surface area of a sphere are numerically the same. Find the volume
of smallest cylinder in which the sphere is exactly kept.
(a) 54π (b) 27π (c )36π (d) 9π
Q30. The volume of the largest right circular cone that can be cut out from a cube of edge 4.2
cm is
(a) 9.7 cm3 (b) 77.6 cm3 (c) 58.2 cm3 (d) 19.4 cm3
ANSWER KEY
Q1(d),
Q2 (b),
Q3 (b),
Q4 (a),
Q5 (b) 4𝜋𝑟2,
Q6 (a) 27:8,
Q7 (b) 9:25,
Q8 (a) 1:2:3,
Q9, (d) 5832 cm3
Q10. (d) Hemisphere + cone
Q11. (c) Cone itself
Q12. (a) 4 π r 2
Q13. (c) Remains unchanged
Q14. (c) 2πrh + 4πr 2
Q15. (c) Sphere
Q16. (a) a cone and a cylinder
Q17. (b) 10a 2
Q18. (d) 4πrh + 2πr 2
Q19. ( d) none of the above
Q20. ( a) 572 cm2
Q21. ( a) 7 cm
Q22. ( d) 44 m2
Q23. ( b) Rs 22000
Q24. ( c) 52.75 cm2
Q25. ( a) 142296
Q26. (a) 16 dm, 8 dm, 4 dm
Q27. (b) Rs 1155
Q28. 33.1%
Q29. 54∏
Q30. 19.4 cm3
