Selina solutions for Concise Mathematics [English] Class 9 ICSE chapter 20 - Solids [Surface Area and Volume of 3-D Solids] [Latest edition]

The area of a square on the diagonal of a cube is 48 cm². Each edge of the cube is ______.

A cuboid has length = 4 cm, breadth = 3 cm and diagonal = 13 cm. The volume of the cuboid is ______.

A cuboid with dimensions 12 cm × 9 cm × 2 cm is made of a metal. It is melted and recast into a solid cube. The edge of the cube is ______.

The dimensional ratio of the sides of a cuboid is 3 : 2 : 1. If its volume is 1296 cm³: the actual dimensions of the cuboid are ______.

A tank with dimensions 12 m, 10 m and 8 m is dug and the soil taken out of it is spread uniformly on a field of length = 40 m and breadth = 32 m. The rise in level of the field is ______.

Through the pipe of uniform cross-section (12 cm²) water flows with the speed of 20 cm/s. The volume of water that flows in 1 minute is ______.

In the given figure, all the dimensions are given in cm. The volume of the solid is:

The length, breadth and height of a rectangular solid are in the ratio 5 : 4 : 2. If the total surface area is 1216 cm², find the length, the breadth and the height of the solid.

The volume of a cube is 729 cm³. Find its total surface area.

The dimensions of a Cinema Hall are 100 m, 60 m, and 15 m. How many persons can sit in the hall if each requires 150 m³ of air? 

75 persons can sleep in a room 25 m by 9.6 m. If each person requires 16 m³ of the air; find the height of the room. 

The edges of three cubes of metal are 3 cm, 4 cm, and 5 cm. They are melted and formed into a single cube. Find the edge of the new cube. 

Three cubes, whose edges are x cm, 8 cm, and 10 cm respectively, are melted and recast into a single cube of edge 12 cm. Find 'x'.

Three equal cubes are placed adjacently in a row. Find the ratio of the total surfaced area of the resulting cuboid to that of the sum of the total surface areas of the three cubes.

The cost of papering the four walls of a room at 75 paise per square meter Rs. 240. The height of the room is 5 meters. Find the length and the breadth of the room, if they are in the ratio 5 : 3. 

The area of a playground is 3650 m². Find the cost of covering it with gravel 1.2 cm deep, if the gravel costs Rs. 6.40 per cubic metre.

A square plate of side 'x' cm is 8 mm thick. If its volume is 2880 cm³; find the value of x.

The external dimensions of a closed wooden box are 27 cm, 19 cm, and 11 cm. If the thickness of the wood in the box is 1.5 cm; find:

1. The volume of the wood in the box;
2. The cost of the box, if wood costs Rs. 1.20 per cm³;
3. A number of 4 cm cubes that could be placed into the box.

A tank 20 m long, 12 m wide and 8 m deep is to be made of iron sheet. If it is open at the top. Determine the cost of iron-sheet, at the rate of Rs. 12.50 per meter, if the sheet is 2.5 m wide.

A closed rectangular box is made of wood of 1.5 cm thickness. The exterior length and breadth are respectively 78 cm and 19 cm, and the capacity of the box is 15 cubic decimeters. Calculate the exterior height of the box.

The square on the diagonal of a cube has an area of 1875 sq. cm. Calculate:
(i) The side of the cube.
(ii) The total surface area of the cube.

The following figure shows a solid of uniform cross-section. Find the volume of the solid. All measurements are in centimeters.

Assume that all angles in the figures are right angles.

A swimming pool is 40 m long and 15 m wide. Its shallow and deep ends are 1.5 m and 3 m deep respectively. If the bottom of the pool slopes uniformly, find the amount of water in liters required to fill the pool.

The cross-section of a tunnel perpendicular to its length is a trapezium ABCD as shown in the following figure; also given that:

AM = BN; AB = 7 m; CD = 5 m. The height of the tunnel is 2.4 m. The tunnel is 40 m long. Calculate:

(i) The cost of painting the internal surface of the tunnel (excluding the floor) at the rate of Rs. 5 per m² (sq. meter).

(ii) The cost of paving the floor at the rate of Rs. 18 per m².

Water is discharged from a pipe of a cross-section area 3.2 cm² at the speed of 5m/s. Calculate the volume of water discharged: 
(i) In cm³ per sec.
(ii) In liters per minute.

A hose-pipe of cross-section area 2 cm² delivers 1500 liters of water in 5 minutes. What is the speed of water in m/s through the pipe? 

The cross-section of a piece of metal 4 m in length is shown below. Calculate :


(i) The area of the cross-section;
(ii) The volume of the piece of metal in cubic centimeters.

If 1 cubic centimeter of the metal weighs 6.6 g, calculate the weight of the piece of metal to the nearest kg.

A rectangular water-tank measuring 80 cm x 60 cm is filled form a pipe of cross-sectional area 1.5 cm², the water emerging at 3.2 m/s. How long does it take to fill the tank?

The radius of a sphere is 2r, then its volume will be ______.

The total surface area of a cube is 96 cm². The volume of the cube is ______.

If a solid cube of side 16 cm is cut into eight identical cubes. The side of each cube is ______.

The diameters of two solid spheres are in the ratio 5 : 7. The ratio between areas of their curved surfaces is ______.

The radius of a cylinder is doubled and its curved surface area is kept as same, the height of the cylinder is ______.

Statement (1): Each side of a cuboid is doubled, its total surface area is also doubled.

Statement (2): The surface area of the resulting cuboid is 2 × 2 × 2 times the original area.

Assertion (A): The radius of a hemisphere increases from r cm to 2r cm. The ratio between the surface areas of the original hemisphere and the resulting hemisphere is 1 : 4.

Reason (R): Surface area in the first case = πr² + 2πr² and surface area in the second case = π(2r)² + 2π(2r)².

Assertion (A): A sphere is inscribed in a cylinder, the ratio of the volume of the cylinder to the volume of the sphere is 1 : 4.

Reason (R): Required ratio 4 = `πr^2 xx 2r : 4/3 πr^3`.

A hollow square-shaped tube open at both ends is made of iron. The internal square is of 5 cm side and the length of the tube is 8 cm. There are 192 cm³ of iron in this tube. Find its thickness.

Four identical cubes are joined end to end to form a cuboid. If the total surface area of the resulting cuboid as 648 m²; find the length of the edge of each cube. Also, find the ratio between the surface area of the resulting cuboid and the surface area of a cube.

A rectangular cardboard sheet has length 32 cm and breadth 26 cm. Squares each of side 3 cm, are cut from the corners of the sheet and the sides are folded to make a rectangular container. Find the capacity of the container formed.

A swimming pool is 18 m long and 8 m wide. Its deep and shallow ends are 2 m and 1.2 m respectively. Find the capacity of the pool, assuming that the bottom of the pool slopes uniformly. 

The following figure shows a closed victory-stand whose dimensions are given in cm.

Find the volume and the surface area of the victory stand. 

Each face of a cube has a perimeter equal to 32 cm. Find its surface area and its volume.

A school auditorium is 40 m long, 30 m broad and 12 m high. If each student requires 1.2 m² of the floor area; find the maximum number of students that can be accommodated in this auditorium. Also, find the volume of air available in the auditorium, for each student. 

The internal dimensions of a rectangular box are 12 cm x  `x` cm x 9 cm. If the length of the longest rod that can be placed in this box is 17 cm; find `x`.   

The internal length, breadth, and height of a box are 30 cm, 24 cm, and 15 cm. Find the largest number of cubes which can be placed inside this box if the edge of each cube is
(i) 3 cm (ii) 4 cm (iii) 5 cm

A rectangular field is 112 m long and 62 m broad. A cubical tank of edge 6 m is dug at each of the four corners of the field and the earth so removed is evenly spread on the remaining field. Find the rise in level.  

When the length of each side of a cube is increased by 3 cm, its volume is increased by 2457 cm³. Find its side. How much will its volume decrease, if the length of each side of it is reduced by 20%?

A rectangular tank 30 cm × 20 cm × 12 cm contains water to a depth of 6 cm. A metal cube of side 10 cm is placed in the tank with its one face resting on the bottom of the tank. Find the volume of water, in liters, that must be poured in the tank so that the metal cube is just submerged in the water. 

The dimensions of a solid metallic cuboid are 72 cm × 30 cm × 75 cm. It is melted and recast into identical solid metal cubes with each edge 6 cm. Find the number of cubes formed.

Also, find the cost of polishing the surfaces of all the cubes formed at the rate Rs. 150 per sq. m.

The dimensions of a car petrol tank are 50 cm × 32 cm × 24 cm, which is full of petrol. If a car's average consumption is 15 km per liter, find the maximum distance that can be covered by the car. 

The dimensions of a rectangular box are in the ratio 4: 2 : 3. The difference between the cost of covering it with paper at Rs. 12 per m² and with paper at the rate of 13.50 per m² is Rs. 1,248. Find the dimensions of the box. 

The length of the diagonal of a cuboid is `13sqrt2` cm and its volume and total surface area is respectively 780 cm³ and 562 cm². Find the dimension of the cuboid.

A warehouse is a large building which, in general, is used to store goods. The dimensions of a warehouse vary with respect to the goods to be stored.

The dimensions of a particular warehouse are 88 m × 66 m × 5.5 m. Its owner wants to fill it completely with identical cubical cartons of maximum volume.

1. What is the largest cube size that can fit perfectly?
2. What is the volume of the warehouse?
3. What is the volume of the cubical carton?
4. What is the maximum number of cartons that can be stored in the warehouse?

Study the following picture of a study table made by Rohan for his SUPW project with match boxes of each dimension 6 cm by 4 cm by 1.5 cm.

Answer the following:

1. How many match boxes are used to make the table?
2. What is the floor area covered by the table?
3. What is the surface area of the top of the table?
4. What is the total volume of the table?