CBSE Class 10 Surface Areas and Volumes Sure Shot Questions Set J

MCQ 

Question. A cylindrical pencil sharpened at one edge is the combination of
(a) two cylinders
(b) a hemisphere and a cylinder
(c) a cone and a cylinder
(d) frustum of a cone and a cylinder
Answer: (c) a cone and a cylinder

Question. A shuttlecock used for playing badminton has the shape of the combination of
(a) a cylinder and a sphere
(b) a sphere and a cone
(c) a cylinder and a hemisphere
(d) frustum of a cone and a hemisphere
Answer: (d) frustum of a cone and a hemisphere

Question. The slant height of the frustum of a cone having radii of two ends as \( 5 \text{ cm} \) and \( 2 \text{ cm} \) respectively and height \( 4 \text{ cm} \) is
(a) \( \sqrt{26} \text{ cm} \)
(b) \( 5 \text{ cm} \)
(c) \( \sqrt{65} \text{ cm} \)
(d) \( 25 \text{ cm} \)
Answer: (b) \( 5 \text{ cm} \)

Question. The total surface area of a hemispherical solid having radius \( 7 \text{ cm} \) is
(a) \( 462 \text{ cm}^2 \)
(b) \( 294 \text{ cm}^2 \)
(c) \( 588 \text{ cm}^2 \)
(d) \( 154 \text{ cm}^2 \)
Answer: (a) \( 462 \text{ cm}^2 \)

Question. A solid formed on revolving a right angled triangle about its height is
(a) cylinder
(b) sphere
(c) right circular cone
(d) two cones
Answer: (c) right circular cone

Question. The surface area of a sphere is \( 616 \text{ cm}^2 \). Its radius is
(a) \( 7 \text{ cm} \)
(b) \( 14 \text{ cm} \)
(c) \( 21 \text{ cm} \)
(d) \( 28 \text{ cm} \)
Answer: (a) \( 7 \text{ cm} \)

Question. A cylinder and a cone are of same base radius and of same height. The ratio of the volume of the cylinder to that of the cone is
(a) \( 2 : 1 \)
(b) \( 3 : 1 \)
(c) \( 2 : 3 \)
(d) \( 3 : 2 \)
Answer: (b) \( 3 : 1 \)

Question. The volume of a sphere is \( 4851 \text{ cm}^3 \). Its diameter is
(a) \( 3.5 \text{ cm} \)
(b) \( 7 \text{ cm} \)
(c) \( 14 \text{ cm} \)
(d) \( 21 \text{ cm} \)
Answer: (d) \( 21 \text{ cm} \)

Question. A piece of paper is in the shape of a semi-circular region of radius \( 10 \text{ cm} \). It is rolled to form a right circular cone. The slant height is
(a) \( 5 \text{ cm} \)
(b) \( 10 \text{ cm} \)
(c) \( 15 \text{ cm} \)
(d) \( 20 \text{ cm} \)
Answer: (b) \( 10 \text{ cm} \)

Question. The base radii of two circular cones of the same height are in the ratio \( 3 : 5 \). The ratio of their volumes are
(a) \( 9 : 25 \)
(b) \( 5 : 3 \)
(c) \( 9 : 5 \)
(d) \( 3 : 25 \)
Answer: (a) \( 9 : 25 \)

Question. The curved surface area of glass having radii \( 3 \text{ cm} \) and \( 4 \text{ cm} \) respectively and slant height \( 10 \text{ cm} \) is
(a) \( 55 \text{ cm}^2 \)
(b) \( 110 \text{ cm}^2 \)
(c) \( 220 \text{ cm}^2 \)
(d) \( 440 \text{ cm}^2 \)
Answer: (c) \( 220 \text{ cm}^2 \)

Question. If two solid hemispheres of same base radius are joined together along their bases, then curved surface area of this new solid is
(a) \( 3\pi r^2 \)
(b) \( 4\pi r^2 \)
(c) \( 5\pi r^2 \)
(d) \( 6\pi \)
Answer: (b) \( 4\pi r^2 \)

Question. The radii of the top and bottom of a bucket of slant height \( 13 \text{ cm} \) are \( 9 \text{ cm} \) and \( 4 \text{ cm} \) respectively. The height of the bucket is
(a) \( 10 \text{ cm} \)
(b) \( 12 \text{ cm} \)
(c) \( 15 \text{ cm} \)
(d) \( 16 \text{ cm} \)
Answer: (b) \( 12 \text{ cm} \)

Question. The shape of an ice-cream cone is a combination of:
(a) Sphere + cylinder
(b) Sphere + cone
(c) Hemisphere + cylinder
(d) Hemisphere + cone
Answer: (d) Hemisphere + cone

Question. If a cone is cut parallel to the base of it by a plane in two parts, then the shape of the top of the cone will be a:
(a) Sphere
(b) Cube
(c) Cone itself
(d) Cylinder
Answer: (c) Cone itself

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

Question. Assertion: the lateral surface area of a right cone is \( 62.82 \) if the radius is \( 4 \text{ cm} \) and the slant height is \( 5 \text{ cm} \).
Reason: lateral surface area of cone = \( \pi rl \)
(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) both Assertion and reason are correct and reason is correct explanation for Assertion

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

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

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

Short Answer Type -1 

Question. A tent is in the form of a cylinder surmounted by a conical top. If the height and radius of cylindrical part are \( 2.8 \text{ m} \) and \( 2 \text{ m} \) and slant height of the top is \( 3.2 \text{ m} \), find the area of canvas used for the tent.
Answer: \( 572 \text{ cm}^2 \)

Question. A cylindrical reservoir is \( 21 \text{ m} \) in diameter. Water is passed into it at \( 420 \text{ litres} \) per minute. Find the rise of water level is the reservoir per hour.
Answer: \( 214.5 \text{ cm}^2 \)

Question. A sphere of radius \( 5 \text{ cm} \) is dropped into a cylindrical vessel partly filled with water. The diameter of the base of vessel is \( 20 \text{ cm} \). If the sphere is completely submerged, find the rise of level of water.
Answer: \( 332.5 \text{ cm}^2 \)

Question. From solid right circular cylinder with height \( 12 \text{ cm} \) and radius of base \( 5 \text{ cm} \), a right circular cone of the same height & same base is cut. Find the volume of the remaining solid.
Answer: \( 66 \text{ cm}^3 \)

Short Answer Type - 2 

Question. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is \( 14 \text{ cm} \) and the total height of the vessel is \( 13 \text{ cm} \). Find the inner surface area of the vessel.
Answer: \( 572 \text{ cm}^2 \)

Question. A toy is in the form of a cone of radius \( 3.5 \text{ cm} \) mounted on a hemisphere of same radius. The total height of the toy is \( 15.5 \text{ cm} \). Find the total surface area of the toy.
Answer: \( 214.5 \text{ cm}^2 \)

Question. A cubical block of side \( 7 \text{ cm} \) is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
Answer: \( 332.5 \text{ cm}^2 \)

Question. A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
Answer: \( \frac{l^2}{4}(\pi + 24) \)

Question. A solid iron pole consists of a cylinder of height \( 220 \text{ cm} \) and base diameter \( 24 \text{ cm} \), which is surmounted by another cylinder of height \( 60 \text{ cm} \) and radius \( 8 \text{ cm} \). Find the mass of the pole, given that \( 1 \text{ cm}^3 \) of iron has approximately \( 8 \text{ g} \) mass. (Use \( \pi = 3.14 \))
Answer: \( 111532.8 \text{ cm}^3 \)

Long Answer 

Question. A juice seller was serving his customers using glasses as shown in Fig. The inner diameter of the cylindrical glass was \( 5 \text{ cm} \), 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 \( 10 \text{ cm} \), find the apparent capacity of the glass and its actual capacity. (Use \( \pi = 3.14 \).)
Answer: \( 163.54 \text{ cm}^2 \)

Question. A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is \( 2 \text{ cm} \) and the diameter of the base is \( 4 \text{ cm} \). 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 \( \pi = 3.14 \))
Answer: \( 25.12 \text{ cm}^3 \)

Question. A copper wire, \( 3 \text{ mm} \) in diameter, is wound about a cylinder whose length is \( 12 \text{ cm} \), and diameter \( 10 \text{ cm} \), 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 \( 8.88 \text{ g per cm}^3 \).
Answer: \( 1256 \text{ cm}; 788 \text{g} \) (approx.)

Question. A right triangle, whose sides are \( 3 \text{ cm} \) and \( 4 \text{ cm} \) (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 \( \pi \) as found appropriate.)
Answer: \( 30.14 \text{ cm}^3; 52.75 \text{ cm}^2 \)

Question. The height of a cone is \( 42 \text{ cm} \). 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: \( 10.5 \text{ cm} \)

Question. A sector of circle of radius \( 15 \text{ cm} \) has the angle \( 120^\circ \). It is rolled up so that two boundary radii are joined together to form a cone. Find the volume of cone.
Answer: \( \frac{250\sqrt{2}}{3} \text{ cm}^3 \)

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 \( 13.5 \text{ m} \) and \( 28 \text{ m} \). If the height of the cylindrical portion is \( 3 \text{ m} \), find the total surface area of the tent.
Answer: \( 287\pi \text{ cm}^2 \)

Question. A cistern, internally measuring \( 150 \text{ cm} \times 120 \text{ cm} \times 110 \text{ cm} \), has \( 129600 \text{ cm}^3 \) 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 \( 22.5 \text{ cm} \times 7.5 \text{ cm} \times 6.5 \text{ cm} \)?
Answer: \( 1792 \)

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 \( 38808 \text{ cm}^3 \) and 11 cylindrical shapes, each of volume \( 1540 \text{ cm}^3 \) with length \( 10 \text{ cm} \). Based on the above information, answer the following questions.

Question. Diameter of the base of the cylinder is
Answer: \( 14 \text{ cm} \)

Question. Diameter of the sphere is
Answer: \( 42 \text{ cm} \)

Question. Total volume of the shape formed is
Answer: \( 55748 \text{ cm}^3 \)

Question. Curved surface area of the one cylindrical shape is
Answer: \( 440 \text{ cm}^2 \)

Question. Total area covered by cylindrical shapes on the surface of sphere is
Answer: \( 539\pi \text{ cm}^2 \)

Case Study : 2

Ajay is a Class X student. His class teacher Mrs Kiran arranged a historical trip to great Stupa of Sanchi. She explained that Stupa of Sanchi is great example of architecture in India. Its base part is cylindrical in shape. The dome of this stupa is hemispherical in shape, known as Anda. It also contains a cubical shape part called Hermika at the top. Path around Anda is known as Pradakshina Path.

Question. Find the lateral surface area of the Hermika, if the side of cubical part is \( 8 \text{ m} \).
Answer: \( 256 \text{ m}^2 \)

Question. The diameter and height of the cylindrical base part are respectively \( 42 \text{ m} \) and \( 12 \text{ m} \). If the volume of each brick used is \( 0.01 \text{ m}^3 \), then find the number of bricks used to make the cylindrical base.
Answer: \( 16,63,200 \text{ bricks} \)

Question. Find the Curved surface area of Anda if its radius is \( 21 \text{ m} \).
Answer: \( 882\pi \text{ cm}^2 \)

CASE STUDY : 3

One day Rinku was going home from school, saw a carpenter working on wood. He found that he is carving out a cone of same height and same diameter from a cylinder. The height of the cylinder is \( 24 \text{ cm} \) and base radius is \( 7 \text{ cm} \). While watching this, some questions came into Rinkus mind. Help Rinku to find the answer of the following questions.

Question. After carving out cone from the cylinder,
(a) Volume of the cylindrical wood will decrease.
(b) Height of the cylindrical wood will increase.
(c) Volume of the cylindrical wood will increase.
(d) Radius of the cylindrical wood will decrease.
Answer: (a) Volume of the cylindrical wood will decrease.

Question. Find the slant height of the conical cavity so formed.
Answer: \( 25 \text{ cm} \)

Question. The curved surface area of the conical cavity so formed is
Answer: \( 175\pi \text{ cm}^2 \)

Question. External curved surface area of the cylinder is
Answer: \( 336\pi \text{ cm}^2 \)

Question. Volume of conical cavity is
Answer: \( 392\pi \text{ cm}^3 \)

CASE STUDY : 4

To make the learning process more interesting, creative and innovative, Amayras class teacher brings clay in the classroom, to teach the topic - Surface Areas and Volumes. With clay, she forms a cylinder of radius \( 6 \text{ cm} \) and height \( 8 \text{ cm} \). Then she moulds the cylinder into a sphere and asks some questions to students.

Question. The radius of the sphere so formed is
Answer: \( 6 \text{ cm} \)

Question. The volume of the sphere so formed is
Answer: \( 288\pi \text{ cm}^3 \)

Question. Find the ratio of the volume of sphere to the volume of cylinder.
Answer: \( 1 : 1 \)

Question. Total surface area of the cylinder is
Answer: \( 28\pi \text{ cm}^2 \)

Question. During the conversion of a solid from one shape to another the volume of new shape will
Answer: Same

CASE STUDY : 5

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 \( 20 \text{ cm} \times 15 \text{ cm} \times 5 \text{ cm} \) and the radius and depth of each conical depression must be \( 0.6 \text{ cm} \) and \( 2.1 \text{ cm} \) respectively. Based on the above information, answer the following questions.

Question. The volume of the cuboidal part is
Answer: \( 1500 \text{ cm}^3 \)

Question. Total volume of conical depressions is
Answer: \( 2.376 \text{ cm}^3 \)

Question. Volume of the wood used in the entire stand is
Answer: \( 1497.624 \text{ cm}^3 \)

Question. If the cost of wood used is Rs \( 0.05 \) per \( \text{ cm}^3 \), then the total cost of making the pen stand is ---
Answer: Rs \( 748.80 \) approx