Please refer to the **MCQ Questions for Class 10 Maths Surface Area and Volume **with Answers. The following Surface Area and Volume Class 10 Maths MCQ Questions have been designed based on the current academic year syllabus and examination guidelines for Class 10. Our faculty has designed MCQ Questions for Class 10 Maths with Answers for all chapters as per your NCERT Class 10 Mathematics book.

## Surface Area and Volume Class 10 MCQ Questions with Answers

Please see below Surface Area and Volume Class 10 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

**Question. The lateral surface area of a cylinder is 176 cm ^{2} and its base area is 38.5cm^{2}. What is its volume?**

(a) 830 cm

^{3}

(b) 380 cm

^{3}

(c) 308 cm

^{3}

(d) 803 cm

^{3}

## **Answer**

C

**Question.** From a circle of radius 15 cm, a sector central angle 216^{O} 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) 1061.9cm^{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

(b) 1 cm

## **Answer**

D

** 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.****The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume is 1/27 . the volume of cone, what is the height at which the section is made?**

(a) 10 cm

(b) 15 cm

(c) 20 cm

(d) 19 cm

## **Answer**

C

** Question.** The cost of painting the curved surface area of a cone at 5 ps / cm

^{2}is ` 35.20, find the volume of the cone if its slant height is 25 cm.

(a) 1223cm

^{3}

(b) 1232cm

^{3}

(c) 1 323cm

^{3}

(d) 1332cm

^{3}

## **Answer**

B

**Question.** The ratio of base radius and height of a cone is 3 :4. If the cost of smoothening the curved surface area at 5 paise/sq cm is `115.50, find the volume of cone.

(a) 12963cm^{3}

(b) 12693cm^{3}

(c) 12936cm^{3}

(d) 12639cm^{3}

## **Answer**

C

** Question.** Rain water from a roof 22 m X 20 m drains into a cylindrical vessel with diameter of base 2 m and height 3.5 m. If the vessel is just full, find the amount of rainfall in cm.

(a) 4.5 cm

(b) 2.5 cm

(c) 3 cm

(d) 1 cm

## **Answer**

B

** Question. The side of a solid metallic cube is 50 cm. It is melted and recast into 8000 similar solid cubical dice. Find the side of each die. **(a) 2.5 cm

(b) 6 cm

(c) 1.9cm

(d) 5.2cm

## **Answer**

A

** Question.** A bucket of height 16 cm made up of metal sheet is in the form of frustum of a right circular cone with radii of its lower and upper ends as 3 cm and 15 cm respectively. What is the slant height of the bucket?

(a) 15 cm

(b) 20 cm

(c) 5 cm

(d) 12 cm

## **Answer**

B

**Question.** A hemispherical bowl of internal diameter 36 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 3 cm and height 9 cm. How many bottles are required to empty the bowl?

(a) 24

(b) 35

(c) 12

(d) 48

## **Answer**

D

**Question.** The largest right circular cone is carved out of a cube whose edge is of length ‘p’ units. Find the volume of the cone. (a) 𝝅p^{3}/12 cu units

(b) 𝝅p^{3}/4 cu units

(c) 𝝅p^{3} cu units

(d) 𝝅p^{3}/5 cu units

## **Answer**

A

**Question.** The ratio of the radii of two spheres is 3 : 2. Find the ratio of their volumes.

(a) 25 : 4

(b) 5 : 16

(c) 9 :14

(d) 27 : 8

## **Answer**

D

**Question. A right-angled triangle ABC, where ∠B = 90 ^{o} , is rotated about BC. If BC = 16 cm and AC = 20 cm, find the volume of the right circular cone traced out by the triangle.**

(a) 2413cm^{3}

(b) 2311 cm^{3}

(c) 1254cm^{3}

(d) 1725cm^{3}

** ****Answer**

**Answer**

A

**Question. The internal and external radii of a hemispherical metallic vessel are 7 cm and 10.5 cm respectively. If 3 1 cm of the metal weighs 10 g, find the weight of the vessel. **

(a) 25.15 kg

(b) 32.1 kg

(c) 17.07 kg

(d) 16.27 kg

**Answer**

C

**Question. A sphere, of diameter 12 cm, is dropped into a right circular cylindrical vessel, partly filled with water. If the sphere is completely immersed in water, the water level in the cylindrical vessel rises by 3,5/9 cm. Find the diameter of the cylindrical vessel. **

(a) 16cm

(b) 18cm

(c) 12cm

(d) 13cm

**Answer**

B

**Question. The ratio of base radius and height of a cone is 3 :4. If the cost of smoothening the curved surface area at 5 paise/sq cm is ₹ 115.50, find the volume of cone. **

(a) 12963cm^{3}

(b) 12693cm^{3}

(c) 12936cm^{3}

(d) 12639cm^{3}

**Answer**

C

**Question. A tent is made in the form of a frustrum A of a right circular cone surmounted by another right circular cone B. The diameter of the ends of the frustrum A are 8 m and 4 m, its height is m ^{3} and the height of the cone B is m^{2}. What is the area of the canvas required for the tent? **

(a) 86.75 m

^{2}

(b) 85.77 m

^{2}

(c) 86.77 m

^{2}

(d) 87.67 m

^{2}

**Answer**

B

**Question. The side of a solid metallic cube is 50 cm. It is melted and recast into 8000 similar solid cubical dice. Find the side of each die. **

(a) 2.5 cm

(b) 6 cm

(c) 1.9cm

(d) 5.2cm

**Answer**

A

**Question. If the radii of the circular ends of a conical bucket of height 45 cm are 28 cm and 7 cm, what is the capacity of the bucket? **

(a) 48150cm^{3}

(b) 48510cm^{3}

(c) 48105cm^{3}

(d) 48015cm^{3}

**Answer**

B

**Question. The length of the longest rod which can, be kept inside a rectangular box is 27 cm. If the length and the breadth of the box are 23 cm and 10 cm respectively, find its height. **

(a) 8cm

(b) 10cm

(c) 12cm

(d) 14cm

**Answer**

B

**Question. The cost of painting the curved surface area of a cone at 5 ps / cm ^{2} is ₹ 35.20, find the volume of the cone if its slant height is 25 cm. **

(a) 1223cm

^{3}

(b) 1232cm

^{3}

(c) 1 323cm

^{3}

(d) 1332cm

^{3}

**Answer**

B

**Question. A semicircular piece of paper of radius 14 cm is rolled to form a cone of the largest possible size. Find the capacity of the cone. **

(a) 721.5cm^{3}

(b) 645.10cm^{3}

(c) 449.64 cm^{3}

(d) 622.37 cm^{3}

**Answer**

D

**Question. In a solid cylinder of height 10 cm and diameter 8 cm, two equal conical cavities have been made at both its ends. If the diameter of the cavity is 6 cm and height 4 cm, find the volume of the remaining solid in terms of π . **

(a) 95π cm^{3}

(b) 136π cm^{3}

(c) 216π cm^{3}

(d) 192π cm^{3}

**Answer**

B