CHAPTER 12 : SURFACE AREAS AND VOLUMES
CBSE Class 10 Mathematics Standard — 2025 PYQs
Series 30/1 to 30/6 | Unique Questions
Section A: Multiple Choice Questions — 1 Mark
1.
1 Mark
Series 30/3/1 (Q12) & 30/3/2 (Q3)
If the
volumes of two cubes are in the ratio
8 : 125, then the ratio of their
surface areas is:
(A) 8 : 125
(B) 4 : 25
(C) 2 : 5
(D) 16 : 25
2.
1 Mark
Series 30/3/3 (Q5)
The radii
r of a sphere and that of the base of a cone are same.
If their volumes are also same, then the height of the cone is:
(A) r
(B) 2r
(C) 3r
(D) 4r
3.
1 Mark
Series 30/4/1 (Q11)
On the top face of a
wooden cube of side 7 cm,
hemispherical depressions of radius
0.35 cm are to be formed
by taking out the wood. The
maximum number of depressions
that can be formed is:
(A) 400
(B) 100
(C) 20
(D) 10
4.
1 Mark
Series 30/6/1 (Q14) & 30/6/2 (Q16)
If a
cone of greatest possible volume is hollowed out from a
solid wooden cylinder, then the ratio of the volume of remaining
wood to the volume of cone hollowed out is:
(A) 1 : 1
(B) 1 : 3
(C) 2 : 1
(D) 3 : 1
Section A: Assertion–Reason — 1 Mark
5.
1 Mark
Series 30/1/1 (Q20) & 30/1/3 (Q20)
Assertion (A): If we join two hemispheres of same radius along
their bases, then we get a sphere.
Reason (R): Total Surface Area of a sphere of radius r is
3πr².
Note: Assertion is true, but Reason is false as the total surface
area of a sphere is 4πr².
Section C: Short Answer Questions — 3 Marks
6.
3 Marks
Series 30/1/1 (Q30) & 30/1/3 (Q29)
A room is in the form of a
cylinder surmounted by a hemispherical
dome. The base radius of the hemisphere is
half of the height
of the cylindrical part. If the room contains
1408/21 m³ of air, find the height of the cylindrical part.
Use:
π = 22/7.
Section D: Long Answer Questions — 5 Marks
7.
5 Marks
Series 30/3/1 (Q35) & 30/3/2 (Q33)
A vessel is in the form of an
inverted cone. Its height is
8 cm and the radius of its top, which is open, is
5 cm.
It is filled with water up to the brim.
When
lead shots (spheres of radius
0.5 cm) are dropped
into the vessel,
one-fourth of the water flows out.
Find the number of lead shots dropped in the vessel.
8.
5 Marks
Series 30/4/2 (Q35)
A shed is in the form of a
cuboid surmounted by a semi-cylinder.
Dimensions:
Cuboidal part = 10 m × 7 m × 3 m
Diameter of semi-cylinder = 7 m
Find the
cost of the tin sheet required to make the shed at
the rate of
₹70 per square metre, if the shed is
open at the front and closed at the back.
9.
5 Marks
Series 30/4/3 (Q33)
A bat manufacturing company made a
huge bat for charity.
The dimensions are in the form of a
cuboid with a cylindrical
handle at the top.
Cuboid:
Length = 2 m
Width = 0.5 m
Thickness = 0.1 m
Cylindrical part:
Diameter = 0.1 m
Height = 0.7 m
Find:
(i) The volume of wood used.
(ii) The total surface area of the wooden bat.
10.
5 Marks
Series 30/5/1 (Q33) & 30/5/2 (Q35)
(a) From one of the faces of a
solid wooden cube of side
14 cm, maximum number of hemispheres of diameter
1.4 cm
are scooped out.
Find the
total number of hemispheres and the
total surface area of the remaining solid.
OR
(b) From a
solid cylinder of height 24 cm and radius
5 cm, two cones of height
12 cm and radius
5 cm
are hollowed out.
Find the
volume and surface area of the remaining solid.
11.
5 Marks
Series 30/6/1 (Q34)
From one face of a
solid cube of side 14 cm, the
largest possible cone is carved out.
Find the
volume and surface area of the remaining solid.
Use:
π = 22/7, √5 = 2.2.
12.
5 Marks
Series 30/6/2 (Q34)
Riya sharpened her pencil from both ends.
The diameter of the cylindrical and conical part is
4.2 mm.
Height of each conical part = 2.8 mm.
Length of the entire pencil = 105.6 mm.
Find the
total surface area of the pencil.
13.
5 Marks
Series 30/3/3 (Q32) & 30/6/3 (Q33)
Fermentation tanks are designed in the form of a
cylinder mounted on a cone.
Total height = 3.3 m
Height of conical part = 1.2 m
Diameter = 1 m
(i) Find the capacity of the tank.
(ii) If the level of liquid is 0.7 m from the top,
find the surface area of the tank in contact with the liquid.
Section E: Case Study Based Questions — 4 Marks
14.
4 Marks
Series 30/2/1 (Q38), 30/2/2 (Q37) & 30/2/3 (Q36)
Case Study: Rolling Pin
A skilled carpenter joins three cylindrical pieces of wood to
create a rolling pin.
Bigger central part:
Length = 12 cm
Diameter = 7 cm
Two smaller identical ends:
Length = 5 cm each
Diameter = 2.1 cm
(i) Find the volume of the bigger cylindrical part.
(ii) Find the curved surface area of the bigger
cylindrical part.
(iii)
(a) Find the ratio of the volume of the bigger part
to the total volume of the two smaller parts.
OR
(b) Find the sum of the curved surface areas of the
two identical smaller parts.