Contents

**GSEB Solutions for Class 10 mathematics – Surface Areas and Volumes (English Medium)**

### Exercise-14.1

**Question 1:**

A toy is made by mounting a cone onto a hemisphere. The radius of the cone and a hemisphere is 5 cm. The total height of the toy is 17 cm. Find the total surface area of the toy.

**Solution :**

**Question 2:**

A show-piece shown in figure 14.10 is made of two solids – a cube and a hemisphere. The base of the block is a cube with edge 7 cm and the hemisphere fixed on the top has diameter 5.2 cm. Find the total surface area of the piece.

**Solution :**

**Question 3:**

A vessel is in the form of a hemisphere mounted on a hollow cylinder. The diameter of the hemisphere is 21 cm and the height of vessel is 25 cm. If the vessel is to be painted at the rate of ₹ 3.5 per cm^{2}, then find the total cost to paint the vessel from outside.

**Solution :**

**Question 4:**

Chirag made a bird-bath for his garden in the shape of a cylinder with a hemispherical depression at one end, (see the figure 14.11). The height of the cylinder is 1.5 m and its radius is 50 cm. Find the total area of the bird-bath. (π = 3.14)

**Solution :**

**Question 5:**

A solid is composed of a cylinder with hemisperical ends on both the sides. The radius and the height of the cylinder are 20 cm and 35 cm respectively. Find the total surface area of the solid.

**Solution :**

**Question 6:**

The radius of a conical tent is 4 m and slant height is 5 m. How many meters of canvas of width 125 cm will be used to prepare 12 tents ? If the cost of canvas is ₹ 20 per meter, then what is total cost of 12 tents ? (π = 3.14)

**Solution :**

**Question 7:**

If the radius of a cone is 60 cm and its curved surface area is 23.55 m^{2}, then find its slant height. (π = 3.14)

**Solution :**

**Question 8:**

The cost of painting the surface of sphere is ₹ 1526 at the rate of ₹ 6 per m^{2}. Find the radius of sphere.

**Solution :**

### Exercise-14.2

**Question 1:**

The curved surface area of a cone is 550 cm^{2}. If its diameter is 14 cm, find its volume.

**Solution :**

**Question 2:**

A solid is in the form of cone with hemispherical base. The radius of the cone is 15 cm and the total height of the solid is 55 cm. Find the volume of the solid. (π = 3.14)

**Solution :**

**Question 3:**

How many litres of milk can be stored in a cylindrical tank with radius 1.4 m and height 3 m ?

**Solution :**

**Question 4:**

The spherical balloon with radius 21 cm is filled with air. Find the volume of air contained in it.

**Solution :**

**Question 5:**

A solid has hemi-spherical base with diameter 8.5 cm and it is surmounted by a cylinder with height 8 cm and diameter of cylinder is 2 cm. Find the volume of this solid. (π = 3.14)

**Solution :**

**Question 6:**

A playing top is made up of steel. The top is shaped like a cone surmounted by a hemisphere. The total height of top is 5 cm and the diameter of the top is 3.5 cm. Find the volume of the top.

**Solution :**

**Question 7:**

How many litres of petrol will be contained in a closed cylindrical tank with hemisphere at one end having radius 4.2 cm and total height 27.5 cm ?

**Solution :**

**Question 8:**

The capacity of a cylindrical tank at a petrol pump is 57750 litres. If its diameter is 3.5 m, find the height of cylinder.

**Solution :**

**Question 9:**

A hemispherical pond is filled with 523.908 m^{3} of water. Find the maximum depth of pond.

**Solution :**

**Question 10:**

A gulab-jamun contain 40 % sugar syrup in it. Find how much syrup would be there in 50 gulab-jamuns, each shaped like a cylinder with two hemispherical ends with total length 5 cm and diameter 2.8 cm.

**Solution :**

**Question 11:**

The height and the slant height of a cone are 12 cm and 20 cm respectively. Find its volume. (π = 3.14)

**Solution :**

**Question 12:**

Find the total volume of a cone having a hemispherical base. If the radius of the base is 21 cm and height 60 cm.

**Solution :**

**Question 13:**

If the slant height of a cone is 18.7 cm and the curved surface area is 602.8 cm^{2}, find the volume of cone. (π = 3.14)

**Solution :**

**Question 14:**

If the surface area of a spherical ball is 1256 cm^{2}, then find the volume of sphere. (Take π = 3.14)

**Solution :**

### Exercise-14.3

**Question 1:**

A hemispherical bowl of internal radius 12 cm contains some liquid. This liquid is to be filled into cylindrical bottles of diameter 4 cm and height 6 cm. How many bottles can be filled with this liquid ?

**Solution :**

**Question 2:**

A cylindrical container having diameter 16 cm and height 40 cm is full of ice-cream. The ice-cream is to be filled into cones of height 12 cm and diameter 4 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with the ice-cream.

**Solution :**

**Question 3:**

A cylindrical tank of diameter 3 m and height 7 m is completely filled with groundnut oil. It is to be emptied in 15 tins each of capacity 15 litres. Find the number of such tins required.

**Solution :**

**Question 4:**

A cylinder of radius 2 cm and height 10 cm is melted into small spherical balls of diameter 1 cm. Find the number of such balls.

**Solution :**

**Question 5:**

A metallic sphere of radius 15 cm is melted and a wire of diameter 1 cm is drawn from it. Find the length of the wire.

**Solution :**

**Question 6:**

There are 45 conical heaps of wheat, each of them having diameter 80 cm and height 30 cm. To store the wheat in a cylindrical container of the same radius, what will be the height of cylinder ?

**Solution :**

**Question 7:**

A cylindrical bucket, 44 cm high and having radius of base 21 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 33 cm, find the radius and the slant height of the heap.

**Solution :**

### Exercise-14.4

**Question 1:**

A metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metalic sheet. The total vertical height of the bucket is 40 cm and that of cylindrical base is 10 cm, radii of two circular ends are 60 cm and 20 cm. Find the area of the metalic sheet used. Also find the volume of water the bucket can hold. (π = 3.14)

**Solution :**

**Question 2:**

A container, open from the top and made up of a metal sheet is the form of frustum of a cone of height 30 cm with radii 30 cm and 10 cm. Find the cost of the milk which can completely fill container at the rate of ₹ 30 per litre. Also find the cost of metal sheet used to make the container, if it costs ₹ 50 per 100 cm^{2}. (π = 3.14)

**Solution :**

### Exercise-14

**Question 1:**

A tent is in the shape of cylinder surmounted by a conical top. If the height and the radius of the cylindrical part are 3.5 m and 2 m respectively and the slant height of the top is 3.5 m, find the area of the canvas used for making the tent. Also find the cost of canvas of the tent at the rate of ₹ 1000 per m^{2}.

**Solution :**

**Question 2:**

A metallic sphere of radius 5.6 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

**Solution :**

**Question 3:**

How many spherical balls of radius 2 cm can be made out of a solid cube of lead whose side measures 44 cm ?

**Solution :**

**Question 4:**

A hemispherical bowl of internal radius 18 cm contains an edible oil to be filled in cylindrical bottles of radius 3 cm and height 9 cm. How many bottles are required to empty the bowl ?

**Solution :**

**Question 5:**

A hemispherical tank of radius 2.4 m is full of water. It is connected with a pipe which empties it at the rate of 7 litres per second. How much time will it take to empty the tank compeletely ?

**Solution :**

**Question 6:**

A shuttle cock used for playing badminton has the shape of a frustum of a cone mounted on a hemisphere. The external diameter of the frustum are 5 cm and 2 cm. The height of the entire shuttle cock is 7 cm. Find its external surface area.

**Solution :**

**Question 7:**

A fez, the headgear cap used by the trucks is shaped like the frustum of a cone. If its radius on the open side is 12 cm and radius at the upper base is 5 cm and its slant height is 15 cm, find the area of material used for making it. (π = 3.14)

**Solution :**

**Question 8:**

A bucket is in the form of a frustum of a cone with capacity of 12308.8 cm^{3} of water. The radius of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of bucket and the cost of making it at the rate of ₹ 10 per cm^{2}.

**Solution :**

**Question 9:**

Select a proper option (a), (b), (c) or (d) from given option :

**Question 9(1):**

The volume of sphere with diameter 1 cm is ……. cm^{3}.

**Solution :**

**Question 9(2):**

The volume of hemisphere with radius 1.2 cm is …… cm^{3}.

**Solution :**

**Question 9(3):**

The volume of sphere is \(\frac{4}{3}\) It cm^{3}. Then its diameter is …… cm .

**Solution :**

**Question 9(4):**

The volume of cone with radius 2 cm and height 6 cm is ……. cm^{3}.

**Solution :**

**Question 9(5):**

The diameter of the base of cone is 10 cm and its slant height is 17 cm. Then the curved surface area of the cone is ……. cm^{2}.

**Solution :**

**Question 9(6):**

The diameter and the height of the cylinder are 14 cm and 10 cm respectively. Then total surface area is ………. cm^{2}.

**Solution :**

**Question 9(7):**

The ratio of the radii of two cones having equal height is 2 : 3. Then, the ratio of their volumes is……..

**Solution :**

**Question 9(8):**

If the radii of a frustum of a cone are 7 cm and 3 cm and the height is 3 cm, then the curved surface area is …… cm^{2}.

**Solution :**

**Question 9(9):**

The radii of a frustum of a cone are 5 cm and 9 cm and height is 6 cm, then the volume is ……. cm^{3}.

**Solution :**