# MCQs for Mathematics Class 10 with Answers Chapter 13 Surface Area and Volume

Students of class 10 Mathematics should refer to MCQ Questions Class 10 Mathematics Surface Area and Volume with answers provided here which is an important chapter in Class 10 Mathematics NCERT textbook. These MCQ for Class 10 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 10 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 10 Mathematics examination

**Chapter 13 Surface Area and Volume MCQ with Answers Class 10 Mathematics**

MCQ Questions Class 10 Mathematics Surface Area and Volume provided below have been prepared by expert teachers of grade 10. These objective questions with solutions are expected to come in the upcoming Standard 10 examinations. Learn the below provided MCQ questions to get better marks in examinations.

**Question. A spherical object of radius 14 cm is dropped into water contained in a right circular cylindrical vessel of radius 21 cm. If the object is completely immersed, the level of water is raised by : **

(a) 6.5 cm

(b) 7.3 cm

(c) 8.3 cm

(d) none of these

**Answer**

C

**Question. A solid cylinder of brass 8 m high and 4 m in diameter is melted and recast into a cone of diameter 3m. The height of the cone is : **

(a) 42 2/3 m^{ }

(b) 42 m

(c) 45 1/3 m

(d) none of these

**Answer**

A

**Question. A reservoir is in the shape of a frustum of a right circular cone. It is 8 m across at the top and 4m across at the bottom. If it is 6 m deep, then its capacity is : **

(a) 176 m^{3}

(b) 186 m^{3}

(c) 216 m^{3}

(d) 254 m^{3}

**Answer**

A

**Question. Marbles of diameter 1.4 cm are dropped into a cylindrical beaker, of diameter 7 cm, containing some water. The number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm, is: **

(a) 50

(b) 100

(c) 150

(d) 200

**Answer**

C

**Question. A cone and a hemisphere have equal bases and equal volumes. The ratio of their heights is : **

(a) 1 : 2

(b) 2 : 1

(c) 1 : 3

(d) 3 : 1

**Answer**

B

**Question. A cylinder whose height is two-third of its diameter has the same volume as a sphere of radius 4 cm. The radius of the base of the cylinder is : **

(a) 2 cm

(b) 3 cm

(c) 4 cm

(d) 6 cm

**Answer**

C

**Question. The diameter of a copper sphere is 18 cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 108 m, its diameter is : **

(a) 0.3 cm

(b) 0.6 cm

(c) 0.8 cm

(d) none of these

**Answer**

B

**Question. A circus tent is cylindrical to a height of 4 m and conical above it, if its diameter is 105 m and its slant height is 40 m, the total area of the canvas required in m2 is : **

(a) 2560

(b) 3760

(c) 7920

(d) none of these

**Answer**

C

**Question. The volume of a largest sphere which is carved out of a cube of side 21 cm is : **

(a) 3951 cm^{3}

(b) 4851 cm^{3}

(c) 5351 cm^{3}

(d) none of these

**Answer**

B

**Question. A hollow spherical shell is made of density 4/9 g/cm ^{3}. If its internal and external radii are 8 cm and 9 cm respectively, the weight of the shell is : [use π = 3.141] **

(a) 203.91 g

(b) 303.91 g

(c) 403.91 g

(d) 503.91 g

**Answer**

C

**Question. The rainwater from a roof 22 m × 20 m drains into a conical vessel having a diameter of base as 2m and height 3.5 m. If the vessel is just full, the rainfall is : **

(a) 4/5 cm

(b) 5/6 cm

(c) 6/7 cm

(d) none of these

**Answer**

B

**Question. The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform circular cross-section. If the length of the wire is 36 m, its radius is : **

(a) 0.5 mm

(b) 1 mm

(c) 2 mm

(d) 4 mm

**Answer**

B

**Question. The number of spherical bullets each of diameter 2 cm which can be made out of a cube of lead whose edge measures 22 cm is **

(a) 1550

(b) 2050

(c) 2241

(d) 2541

**Answer**

D

**Question. The hight of a right circular cone is 12 cm. If its volume is 100π cm ^{3}, its slant height is: **

(a) 18 cm

(b) 20 cm

(c) 13 cm

(d) none of these

**Answer**

C

**Question. A cone is 8.4 cm high and radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is **

(a) 2 cm

(b) 2.1 cm

(c) 3.5 cm

(d) none of these

**Answer**

B

**Question. A vessel is conical in shape. If its volume is 33.264 litres and height is 72 cm, find the cost of repairing its curved surface area at? 12/sq m. **

(a) ₹ 5.94

(b) ₹ 6.94

(c) ₹ 7.95

(d) ₹ 9.65

**Answer**

A

**Question. A top is of the shape of a cone over a hemisphere. The radius of the hemisphere is 3.5 cm. The total height of the top is 15.5 cm. Find the total area of the top. **

(a) 214.5cm^{2}

(b) 21.45cm^{2}

(c) 215.4cm^{2}

(d) 21.43cm^{2}

**Answer**

A

**Question. From a circle of radius 15 cm, a sector central angle 216° is cut and its bounding radii are joined without overlap so as to form a cone. Find its volume. **

(a) 1081.3cm^{3}

(b) 1071.3cm^{3}

(c) 1018.3cm^{3}

(d) 1 061.9cm^{3}

**Answer**

C

**Question. A cylindrical vessel of diameter 4 cm is partly filled with water. 300 lead balls are dropped in it. The raise in water level is 0.8 cm. Find the diameter of each ball. **

(a) 0.8 cm

(b) 0.4 cm

(c) 0.2 cm

(d) 0.6 cm

**Answer**

B

**Question. 56 circular plates, each of radius 5 cm and thickness 0.25 cm, are placed one above the other to form a solid right circular cylinder. Find the volume of the cylinder so formed. **

(a) 900 cm^{3}

(b) 885 cm^{3}

(c) 1100 cm^{3}

(d) 1250cm^{3}

**Answer**

C

**Question. Three solid glass balls of radii ‘r’ cm, 6 cm and 8 cm are melted into a solid sphere of radius 9 cm. Find the value of ‘r’. **

(a) 1/4 cm

(b)1/3 cm

(c) 1/2 cm

(d) 1 cm

**Answer**

D

**Question. What is the maximum distance between any two points of a cube of side T units? **

(a) (√2 + 1)l units

(b) √2 l units

(c) √3l units

(d) √2l units

**Answer**

C

**Question. The base radius of a cylinder is 1,2/3. times its height. The cost of painting its curved surface area at 2 paise / cm2 is ₹ 92.40. Find the volume of the liquid. **

(a) 80850 cm^{3}

(b) 80580 cm^{3}

(c) 80508 cm^{3}

(d) 800508 cm^{3}

**Answer**

A

**Question. The volume of a cube is numerically equal to its surface area. What is the length of its side? **

(a) 6 units

(b) 8 units

(c) 9 units

(d) 10 units

**Answer**

A

**Question. The radii of circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area. **

(a) 1564.15cm^{2}

(b) 7599.43cm^{2}

(c) 6542.1 cm^{2}

(d) 8265.14cm^{2}

**Answer**

B

We hope the above multiple choice questions for Class 10 Mathematics for Chapter 13 Surface Area and Volume provided above with answers based on the latest syllabus and examination guidelines issued by CBSE, NCERT and KVS are really useful for you. Surface Area and Volume is an important chapter in Class 10 as it provides very strong understanding about this topic. Students should go through the answers provided for the MCQs after they have themselves solved the questions. All MCQs have been provided with four options for the students to solve. These questions are really useful for benefit of class 10 students. Please go through these and let us know if you have any feedback in the comments section.