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## VBQ for Class 10 Mathematics Chapter 13 Surface Areas and Volumes

Class 10 Mathematics students should refer to the following value based questions with answers for Chapter 13 Surface Areas and Volumes in Class 10. These VBQ questions with answers for Class 10 Mathematics will come in exams and help you to score good marks

### Chapter 13 Surface Areas and Volumes VBQ Questions Class 10 Mathematics with Answers

**CHAPTER –SURFACE AREA & VOLUME**

**Question. In a city the corporation supplies water to 35 houses in a street through a cylindrical tank of diameter 42cm and length 105cm.On a particular day due to the leakage in the tank water was sufficient only to 25houses.The people in the street told the water man to distribute the available water to all the 35 houses.**

**CONTEXTUAL QUESTION **

(i) How much water each house gets on any day?

(ii) How much water each house gets on the day there was leakage in the tank?

**VALUE BASED QUESTION**

(iii) What values (any two) the people in the street possess?

**KEY POINTS.**

* Sharing

* Care for others

* Selflessness

* Unity

* Self discipline

* Concern for others

* Responsible citizen

* Right for equality.

**Question. Asha and Usha are two sisters of Rohan. On a Rakhee day Rohan gave 16 Laddus (sweet, Sphere in shape)of diameter 6cm to Asha and 2 laddus of radius 6cm to Usha.**

**CONTEXTUAL QUESTION **

(i) To which sister Rohan gave more sweets?

**VALUE BASED QUESTION **

(ii) What value Rohan possess in distributing the sweets to his sisters?

**KEY POINTS.**

*Impartial

*Responsible

*Concern

*Sensitive

**Question. A Mathematics teacher told the students to make a model solids using the card board. It can be either a hemisphere surmounted by a cone or a hemisphere surmounted by a cylinder(closed on the top). Both the solids have the same total height 17cm and radius 5cm. Cost of card board is 20paise per sq.cm.**

**CONTEXTUAL QUESTION**

**VALUE BASED QUESTION**

**KEY POINTS.**

**Question. In a village, due to heavy rain many people came out of their houses and were made to stay in a school building. Local volunteers prepared 1200 food packets each of dimensions 10 cm x 6cm x 3cm is packed in to 600 boxes to distribute the people.**

**CONTEXTUAL QUESTIOIN**

**VALUE BASED QUESTION**

**KEY POINTS.**

**Question. There are 3 types of bowl namely A, B, C are available in the shop for sale. The cost of each type is the same. Bowl A is hemispherical with radius 6.3cm,bowl B is a frustum of a cone with radii 3cm and 5cm with the height 6cm and bowl C is cylindrical in shape with radius 5cm and height 7cm.Shop keeper gives the cylindrical bowl to the customer.**

**CONTEXTUAL QUESTION**

**VALUE BASED QUESTION**

**KEY POINTS.**

**Question. Ranjith gave a playing top as a gift to his friend Sanju on his birth day. The top is shaped like a cone surmounted by a hemisphere. Total height of the top is 7cm and the radius is 3cm.Ranjith wants to colour the top.**

**CONTEXTUAL QUESTION**

**VALUE BASED QUESTION**

**CASE STUDY BASED **

**Case Study 1. **Arun a 10th standard student makes a project on corona virus in science for an exhibition in his school. In this project, he picks a sphere which has volume 38808 cm^{3} and 11 cylindrical shapes, each of volume 1540 cm^{3} with length 10 cm. Based on the above information, answer the following questions.

**(ii) Diameter of the sphere is ****Answer :**** **42cm

**(iii) Total volume of the shape formed is ****Answer :**** **55748cm^{3}

**(iv) Curved surface area of the one cylindrical shape is ****Answer : **440 cm^{2}

**(v) Total area covered by cylindrical shapes on the surface of sphere is ****Answer :**** **539 𝜋 cm^{2}

**CASE STUDY 2. **A carpenter used to make and sell different kinds of wooden pen stands like rectangular, cuboidal, cylindrical, conical. Aanav went to his shop and asked him to make a pen stand as explained below. Pen stand must be of the cuboidal shape with three conical depressions, which can hold 3 pens. The dimensions of the cuboidal part must be 20 cm x 15 cm x 5 cm and the radius and depth of each conical depression must be 0.6 cm and 2.1cm respectively.

**Based on the above information, answer the following questions.**

**(i) The volume of the cuboidal part is ---------------****Answer :** 1500cm^{3}

**(ii) Total volume of conical depressions is ----------------****Answer :** 2.376 cm^{3}

**(iii) Volume of the wood used in the entire stand is ------------****Answer :** 1497.624 cm^{3}

**(iv) If the cost of wood used is Rs 0.05 per cm ^{3}, then the total cost of making the pen stand is --- **

**Answer :**Rs 748.80 approx)

**ASSERTION REASONING **

**Question. Assertion: a cylinder and right circular cone are having the same base and same height the volume of cylinder is three times the volume of cone****Reason: if the radius of cylinder is doubled and height is halved the volume will be doubled**

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false**Answer : B**

**Question. Assertion: the lateral surface area of a right cone is 62.82 if the radius is 4 cm and the slant height is 5 cm. ****Reason: lateral surface area of cone = πrl**

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false**Answer : A**

**Question. Assertion: the perpendicular distance between two bases is the height of cylinder ****Reason: the line segment joining the centre of two bases is the axis of cylinder**

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false**Answer : B**

**Question. Assertion: volume of cuboid is defined as the amount of space occupied by the walls of cuboid in three dimensional space ****Reason: volume of cuboid is the product of length ,width ,height**

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false**Answer : B**

**Question. Assertion: a sphere is a symmetrical object ****Reason: a sphere had an only a curved surface no flat surface no edge and no vertices**

a) both Assertion and reason are correct and reason is correct explanation for Assertion

b) both Assertion and reason are correct but reason is not correct explanation for Assertion

c) Assertion is correct but reason is false

d) both Assertions and reason are false**Answer : B**

**Very Short Answer type Questions**

**Question. The height of a cone is 42 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume is 1/64 of the volume of the given cone, find the height at which the section is made. Answer : **10.5 cm

**Question. A juice seller was serving his customers using glasses as shown in Fig. The inner diameter of the cylindrical glass was 5 cm, but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10 cm, find the apparent capacity of the glass and its actual capacity. (Use π = 3.14.) ****Answer :** 163.54 cm^{2}

**Question. A cistern, internally measuring 150 cm × 120 cm × 110 cm, has 129600 cm3 of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each brick being 22.5 cm × 7.5 cm × 6.5 cm?. ****Answer :** 1792

**Question. A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference of the volumes of the cylinder and the toy. (Take π = 3.14)****Answer :** 25.12 cm^{3}. 25.12 cm^{3}

**Question. A sector of circle of radius 15 cm has the angle 120°. It is rolled up so that two boundary radii are joined together to form a cone. Find the volume of cone.Answer : ** 250√23𝜋 cm

^{3}

**Question. A right triangle, whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate.) ****Answer : ** 30.14 cm^{3} ; 52.75 cm^{2})

**Question. A tent is in the shape of a right circular cylinder surmounted by a cone. The total height and the diameter of the base are 13.5 m and 28 m. If the height of the cylindrical portion is 3 m, find the total surface area of the tent. ****Answer : ** 287 𝜋 cm^{2}

**Question. A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of copper to be 8.88 g per cm ^{3} . **

**Answer :**1256 cm; 788g app

**Question. 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.****Answer : **160 cm^{2}

**Question. Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length ****is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel ****made. (Assume the outer and inner dimensions of the model to be nearly the same.)Answer : **66 cm

^{3}.

**Question. A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.Answer : **214.5 cm

^{2}

**Question. A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. ****Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.****Answer : **1.131 m3 (approx.)

**Question. A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.Answer : **(1/4)l

^{2}(π +24)

**Question. 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, each of which is a sphere 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.Answer : **100

**Question. From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm ^{2}.Answer : **18 cm

^{2}

**Question. A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.****Answer : **π cm^{3}

**Question. 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.****Answer : **572 cm2

**Question. A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of thepole, given that 1 cm3 of iron has ****approximately 8g mass. (Use π = 3.14)Answer : **892.26 kg

**Question. 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. Also, find the cost of the canvas of the tent at the rate of ₹500 per m ^{2}.Answer : **44 m

^{2}, Rs 22000

**Question. A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds itsvolume to be 345 cm3. Check ****whether she is correct, taking the above as the inside measurements, and π = 3.14.Answer : **Not correct. Correct answer is 346.51 cm

^{3}.

**Question. A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.Answer : **Greatest diameter = 7 cm, surface area = 332.5 cm

^{2}

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### CBSE Class 10 Mathematics Chapter 13 Surface Areas and Volumes VBQs

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