Given below are the

a. Frustrum problems

b. Melt and recasted problems

c. Hemisphere problems

d. Water pipe and tank problems

e. Mixture of shapes problems

If the diameter of cross-section of a wire is decreased by 5% how much how much percent will be the length be increased so that the volume remains the same?

Solution

A solid sphere of radius 3cm is melted and then cast into small balls each of radius 0.3cm. Find the no. of balls thus obtained.

Solution

How many spherical bullets can be made out of a solid cube of lead whose edge measures 44cm, each bullet being 4cm in diameter?

Solution

A canal is 300 cm wide and 120 cm deep. The water in the canal is flowing with a speed of 20 km/h. How much area will it irrigate in 20 minutes if 8 cm of standing water is desired?

Solution

A sphere of diameter 6cm is dropped in a right circular cylindrical vessel partly filled with. The diameter of the cylindrical vessel is 12cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?

Solution

A right circular cone is 3.6cm and the radius of its base is 1.6cm. It is melted and recast into a right circular cone with radius of its base as 1.2cm. Find its height.

Solution

A conical vessel whose internal radius is 5cm and height 24cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10cm. Find the height to which the water rises.

Solution

Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and formed into a single cube.Find the edge of the cube so formed

Solution

Find the number of coins, 1.5cm in diameter and 0.2cm thick, to be melted to form a right circular cylinder of height 10cm and diameter 4.5cm.

Solution

A glass cylinder with diameter 20cm has water to a height of 9cm. A metal cube of 8cm in emerged in it completely. Calculate the height by which water will rise in the cylinder.

Solution

A well, whose diameter is 7cm, has been dug 22.5m deep and the earth dugout is used to form an embankment around it. If the height of the embankment is 1.5m, find the width of the embankment.

Solution

An agriculture field is in the form of a rectangle of length 20m and width 14m. A 10m deep well of diameter 7m is dug in a corner of the field and the earth taken out of the well is spread evenly over the remaining part of the field. Find the rise in the level.

Solution

The perimeters of ends of a frustum are 48cm & 36cm, if height of frustum be 11cm, find its volume.

Solution

A cylindrical pipe has inner diameter of 7cm and water flows through it at 192.5 l/min. Find the rate of flow in kilometers per hour.

Solution

Water is being pumped out through a circular pipe whose internal diameter is 7cm. if the flow of water is 72cm per second, how many liters of water are being pumped out in one hour?

Solution

Water is flowing at the rate of 3km/hr through a circular pipe of 20cm internal into a circular cistern of diameter 10m and depth 2m.In how much time will cistern will be filled?

Solution

Water is flowing at the rate of 7 meters per second through a circular pipe whose internal diameter is 2cm into a cylindrical tank the radius of whose base is 40 cm determine the increase in the water level in ½ hours.

Solution

An inverted cone of vertical height 12cm and radius of the base 9cm has water to a depth of 4cm.Find the area of the internal surface of the cone not in contact with water

Solution

Water is flowing at the rate of 5km /hr through a pipe of diameter 14m into a rectangular tank which is 50m long and 44m wide. Determine the time in which the level of water in the tank will rise by 7cm?

Solution

Water in a canal, 30dm wide and 12dm deep is flowing with velocity of 10km/hr. How much area will it irrigate in30minutes if 8cm of standing water is required for irrigation?

Solution

Water flow at the rate of 10 meters per minute through a cylindrical pipe having the diameter as 5mm. How much time will it take to fill a conical vessel whose diameter of base is 40cm and depth24cm?

Solution

A hemispherical tank of radius 1.75m 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 completely?

Solution

The barrel of a fountain pen, cylindrical in shape, is 7cm long and 5mm in diameter. A full barrel of ink in the pen will be used upon writing 3300 words on an average. How many words can be written in a bottle of ink containing one fifth of a litre?

Solution

The cost of painting the total outside surface of a closed cylindrical oil tank at 60 paise per sq. dm is Rs. 237.60. The height of the tank is 6 times the radius of the base of the tank. Find its volume correct to two decimal places.

Solution

A solid iron rectangular block of dimensions 4.4 m, 2.6m, and 1m is cast into a hollow cylindrical pipe of internal radius 30cm and thickness 5cm. Find the length of the pipe. (Use Π = 22/7)

Solution

A building is in the form of a cylinder surmounted by a hemispherical dome . The base diameter of the dome is equal to 2/3 of the total height of the building. Find the height of the building, if it contains $67 \frac {1}{27} m^3$ of air

Solution

**Notes**-
**Assignments** -
**NCERT Solutions**- NCERT Solution Surface Area and Volume Class10 Exercise 13.1
- NCERT Solution Surface Area and Volume Class10 Exercise 13.2
- NCERT Solution Surface Area and Volume Class10 Exercise 13.3

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