**Assignments**
**NCERT Solutions**
Given below are the

**Class 10 Maths** Important Questions for Surface Area and Volume

a) Concepts questions

b) Calculation problems

c) Multiple choice questions

d) Long answer questions

e) Fill in the blank's

**Question 1)** 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
Original Volume=$\pi R^2 H$

When diameter is decreased by 5%, radius also is decreased by 5%.

New Radius = R - 5R/100 = 95R/100= 19R/20

New Volumne=$\pi (\frac {19R}{20})^2 H = \frac {\pi.H.361R^2}{400}$

But you want to maintain the volume at a constant, so Length H is to be multiplied by 400/361 to keep it constant.

So New Length= 400H/361

Increase in Length=400H/361 -H = 39H/361

% Increase in Length = (39/361) * 100 = 10.8%

**Question 2)** 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
Let number of small balls = x

Volume of x small balls = Volume of sphere

$x \times \frac{4}{3}\pi (.3)^3 = \frac{4}{3} \pi (3)^3$

x=1000

**Question 3)** 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
Edge of the solid cube = 44 cm

Volume of the cube =L^{3}= 44^{3} = 85184 cm^{3}

Diameter of the bullet = 4 cm

Radius = 2 cm

Volume of each bullet = $\frac {4}{3}\pi R^3$

= 33.5 cm^{3}

Number of bullets = 85184 / 33.5 = 2542.8=2542(approx)

**Question 4)** 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
Width 300cm=3m

depth 120cm=1.2m

speed of canal 20km/h= 20×1000m/h

vol. of water flow in 1 hour = width of canal ×depth of canal ×speef of canal water

3×1.2×20×1000=72000m^{3}

So vol. of water flow in 20 min = 72000×20/60=24000m^{3}

Area irrigated in 20 min =240000/0.08=300000m^{2}

**Question 5)** 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?

**Question 6)** 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.

**Question 7)** 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.

**Question 8)** 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

**Question 9)** 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.

**Question 10)** 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.

**Question 11)** 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.

**Question 12)**An agriculture field is in the form of a rectangle of length 20cm and width 14cm. A 10cm deep well of diameter 7cm 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.

**Question 13)** The perimeters of ends of a frustum are 48cm & 36cm, if height of frustum be 11cm, find its volume.

**Question 14)** 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.

**Question 15)** Water is being pumped out through a circular pipe whose internal diameter is 72cm per second, how many liters of water are being pumped out in one hour?

**Question 16)** Water is flowing at the rate of 3km/hr. through a circular pipe 0f 20cm internal into a circular cistern of diameter 10m and depth 2m.In how much time will cistern will be filled?

**Question 17)** 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.

**Question 18)** 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

**Question 19)** 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?

**Question 20)** 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?

**Question 21)** 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?

**Question 22)** 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?

**Question 23)** 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 330 words on an average. How many would use up a battle of ink containing one-fifth of a litre?

**Question 24)** 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.

**Question 25)** A solid iron rectangular block of dimensions 4.4 m, 2.6m, and 1m is cast into a hollow cylindrical pipe wof internal radius 30cm and thickness 5cm. Find the length of the pipe. (Use Π = 22/7)

Other Questions Answers
5) 1cm

6) 6.4cm

7) 2cm

8) 6cm

9) 450

10) 1.6cm

11) 10.5m

12) 1.594m

13) 1554 cm^{3}

14) 3km per hour

15) 9979.2 litres

16) 1 hour 40 minutes

17) 787.5cm

18) 376.8 cm^{2}

19)2.5cm

20)225000m^{2}

21) 51 minutes 12 seconds

22) 26.73 minutes

23) 48000

24) 509.14dm^{3}

25) 112m

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