CBSE Class 10 Mathematics Chapter 13 Surface Areas and Volumes Multiple Choice Questions with Answers. MCQ Class 10 Maths Surface Areas and Volumes with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Mathematics Surface Areas and Volumes MCQs with Answers to know their preparation level.
Multiple Choice Questions - Set - 5
Question 1:
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
Correct Answer – (D)
We know that,
The total surface area of cylinder = 2πrh + 2πr2
When one cylinder is placed over the other cylinder of same height and radius, then height of the new cylinder will be 2h and radius will be r.
Thus, the total surface area of the shape so formed = 2πr(2h) + 2πr2 = 4πrh + 2πr2
Question 2 :
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
(a) 32.7 litres
(b) 33.7 litres
(c) 34.7 litres
(d) 31.7 litres
Correct Answer – (A)
The height of the bucket = h = 35 cm
Diameter of one circular end of bucket = 44 cm
Then the radius R = 22 cm
Diameter of another end = 24 cm
Then the radius r = 12 cm
We know that Volume of the bucket = (1/3)πh[R2 + r2 + Rr]
= (1/3) × (22/7) × 35 × [(22)2 + (12)2 + 22 × 12]
= (35/3) × (22/7) × (484 + 144 + 264)
= (5 × 22 × 892)/3
= 32706.6 cm3
= 32.7 litres.
Question 3 :
A solid piece of iron in the form of a cuboid of dimensions 49 cm × 33 cm × 24 cm, is moulded to form a solid sphere. The radius of the sphere is
(a) 21 cm
(b) 23 cm
(c) 25 cm
(d) 19 cm
Correct Answer – (A)
For the given cuboid,
Length, l = 49 cm
Breadth, b = 33 cm
Height, h = 24 cm
Volume of cube = 49 × 33 × 24 cm3
Let r be the radius of the sphere.
Volume of sphere = 4/3 πr3
Volume of cuboid = volume of sphere molded
49 × 33 × 24 = 4/3 πr3
⇒ πr3 = 29106
⇒ r3 = 29106 × (22/7)
⇒ r3 = 9261
⇒ r3 = (21)3
⇒ r = 21 cm
Hence, the radius of sphere is 21 cm
Question 4 :
A shuttle cock used for playing badminton has the shape of the combination of
(a) a cylinder and a sphere
(b) a cylinder and a hemisphere
(c) a sphere and a cone
(d) frustum of a cone and a hemisphere
Correct Answer – (D)
Question 5 :
If we join two hemispheres of same radius along their bases, then we get a;
(a) Cone
(b) Cylinder
(c) Sphere
(d) Cuboid
Correct Answer – (C)
Question 6 :
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
Correct Answer – (B)
The total surface area of a cube having side a = 6a2
If two identical faces of side a are joined together, then the total surface area of the cuboid so formed is 10a2.
Question 7 :
A right circular cylinder of radius r cm and height h cm (h>2r) just encloses a sphere of diameter
(a) r cm
(b) 2r cm
(c) h cm
(d) 2h cm
Correct Answer – (B)
Radius of cylinder = r
Height = h > 2r
Since the sphere is enclosed by a cylinder, the radius of the cylinder will be the radius of the sphere.
Therefore, diameter of sphere = 2r cm
Question 8 :
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
(a) 142296
(b) 142396
(c) 142496
(d) 142596
Correct Answer – (A)
Volume of cube = 223 = 10648 cm3
Volume of cube that remains unfilled = (1/8) × 10648 = 1331 cm3
volume occupied by spherical marbles = 10648 − 1331 = 9317 cm3
Radius of the spherical marble = 0.5/2 = 0.25 cm = 1/4 cm
Volume of 1 spherical marble = (4/3) × (22/7) × (1/4)3 = 11/168 cm3
Numbers of spherical marbles = n = 9317 × (11/168) = 142296
Question 9 :
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
Correct Answer – (A)
Question 10 :
A tank is made of the shape of a cylinder with a hemispherical depression at one end. The height of the cylinder is 1.45 m and radius is 30 cm. The total surface area of the tank is:
(a) 30 m
(b) 3.3 m
(c) 30.3 m
(d) 3300 m
Correct Answer – (B)
Total surface area of tank = CSA of cylinder + CSA of hemisphere
= 2πrh + 2πr2= 2π r(h + r)
= 2 x 22/7 x 30(145 + 30) cm2
=33000 cm2
= 3.3 m2
- NCERT Solutions Class 10 Mathematics Surface Areas and Volumes : Exercise 13.1
- NCERT Solutions Class 10 Mathematics Surface Areas and Volumes : Exercise 13.2
- NCERT Solutions Class 10 Mathematics Surface Areas and Volumes : Exercise 13.3
- NCERT Solutions Class 10 Mathematics Surface Areas and Volumes : Exercise 13.4
- NCERT Solutions Class 10 Mathematics Surface Areas and Volumes : Exercise 13.5
