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NCERT Solutions for Class 10 Maths Ch 13 Surface Areas and Volumes
NCERT Solutions for Class 9 Mathematics Surface Areas and Volumes. 1. A plastic box m long, m wide and 65 cm deep is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet, determine: (i) The area of the sheet required for making the box. (ii) The cost of sheet for it, if a sheet measuring 1m2 cost Rs� Hence bricks can be painted. NCERT Solutions for Class 9 Maths Exercise 5. A cubical box has each edge 10 cm and a cuboidal box is 10 cm wide, cm long and 8 cm high. (i) Which box has the greater lateral surface area and by how much? (ii) Which box has the smaller total surface area and how much? Ans. (i) Lateral surface area of a cube = 4 (side)2 = 4 x (10)2 = cm2. Lateral surface area of a cuboid. The Class 10th Maths textbook consists of total 15 chapters which can be divided into seven units. There are various questions provided between the chapter known as NCERT Solutions. These NCERT questions are important for the purpose of examinations and also help in developing your knowledge.� These study materials will save your time and you can study effectively. NCERT Solutions for Class 10 Maths are explained properly giving you concepts of different topics. Maths is a subject of practice so you must try not to repeat the mistakes that you have done in the exam earlier and to learn from those mistakes. Download NCERT Solutions for other subjects here. Download NCERT Solutions for Class 10 Maths Chapterwise here. Surface Areas and Volumes � Exercise This exercise covers the surface areas of the combination of different solids. Furthermore, these shapes can be a combination of a cylinder and sphere, a cone and a sphere, a cylinder, and a cone, and many more combinations.

Our experts have updated these solutions according to the latest pattern of CBSE. The surface area of the solid is 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. Two hemisphere and one cylinder are given in the figure. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in figure.

If the height of the cylinder is 10 cm and its base is of radius 3. Exercise 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.

Given, solid is a combination of a cone and a hemisphere. 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 mode. Assume the outer and inner dimensions of the model to be nearly the same. Given, model is a combination of a cylinder and two cones.

Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2. Let r be the radius of the hemisphere and cylinder both.

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.

The radius of each of the depressions is 0. Find the volume of wood in the entire stand see figure. 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 upto the brim. When lead shots, each of which is a sphere of radius 0. Find the number of lead shots dropped in the vessel.

A solid iron pole consists of a cylinder of height cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm 3 of iron has approximately 8 g mass. A solid consisting of a right circular cone of height 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 cm. A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8. By measuring the amount of water it holds, a child finds its volume to be.

A metallic sphere of radius 4. Find the height of the cylinder. Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere. Let r1, r2 and r3 be the radius of given three spheres and R be the radius of a single solid sphere. A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m.

Find the height of the platform. A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4m to form an embankment. Find the height of the embankment. A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream.

The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream. Let the height and radius of ice cream container cylinder be h1 and r1. How many silver coins, 1.

We know that, every coin has a shape of cylinder. Let radius and height of the coin are r1 and h1 respectively. A cylindrical bucket, 32 cm high and with radius of base 18 cm, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap. Let the radius and slant height of the heap of sand are r and l. Water in a canal, 6 m wide and 1.

How much area will it irrigate in 30 minutes, if 8 cm of Ncert Class 10th Exercise 13.1 Lyrics standing water is needed? A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep.

A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass. The slant height of a frustum of a cone is 4 cm and the perimeters circumference of its circular ends are 18 cm and 6 cm.

Find the curved surface area of the frustum. Let the slant height of the frustum be l and radius of the both ends of the frustum be r1 and r2. A fez, the cap used by the turks, is shaped like the frustum of a cone see figure.

If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it. Let the slant height of fez be l and the radius of upper end which is closed be r1 and the other end which is open be r2.

A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Also find the cost of metal sheet used to make the container. Let h be the height of the container, which is in the form of a frustum of a cone whose lower end is closed and upper end is opened.

Also, let the radius of its lower end be r1 and upper end be r2. Let r1 and r2 be the radii of the frustum of upper and lower ends cut by a plane. 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. When a wire is one round wound about a cylinder, it covers a 3 mm of length of the cylinder. 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. 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. In one fortnight of a given month, there was a rainfall of 10 cm in a river valley.

If the area of the valley is km 2 , show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each km long, 75 m wide and 3 m deep. An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone.

If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel. Given, oil funnel is a combination of a cylinder and a frustum of a cone. Derive the formula for the curved surface area and total surface area of the frustum of a cone.

Using the symbols as explained. We complete the conical part OCD. Let slant height of the cone OAB be l 1 and its height be h 1 i. Derive the formula for the volume of the frustum of a cone given to you in the section Let the height of the cone OAB be h 1 and its slant height be l 1.

Chapter 13 Class 10 Maths NCERT Solutions plays very important role during the preparation of board exams as a lot of questions from this topic can be asked. There are total 5 topics in this chapter which will guide students in a better way. We are going to learn about how to find surface areas and volumes of these types of objects. The total surface area of the new solid is the sum of the curved surface areas of each of the individual parts.

The volume of the solid formed by joining two basic solids will be the sum of the volumes of the constituents. In this topics, we will dealing with the questions based on finding the volume of a frustum of a cone.

How many exercises in Chapter 13 Surface Areas and Volumes There are total 5 exercise in the Chapter 13 Surface Areas and Volumes which will make students while solving any questions. These are also useful for competitive exams and higher grades. What do you mean by Cube? What is lateral surface area of cuboid? Is it true?

Main points:

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