CHAP13_EX13.5_1. 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 8.88 g per cm3
CHAP13_EX13.5_3. A cistern, internally measuring 150 cm × 120 cm × 110 cm, has 129600 cm3
of water in it. 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. How many bricks can be put in
without overflowing the water, each brick being 22.5 cm × 7.5 cm × 6.5 cm?
CHAP13_EX13.5_4. 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 7280 km2, show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.
CHAP13_EX13.3_7.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.
CHAP13_EX13.3_8. Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?
CHAP13_EX13.3_9. 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. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled
CHAP13_EX13.3_Selvi’s house has an overhead tank in the shape of a cylinder. This
is filled by pumping water from a sump (an underground tank) which is in the
shape of a cuboid. The sump has dimensions 1.57 m × 1.44 m × 95cm. The
overhead tank has its radius 60 cm and height 95 cm. Find the height of the water
left in the sump after the overhead tank has been completely filled with water
from the sump which had been full. Compare the capacity of the tank with that of
the sump. (Use π = 3.14
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A reducing agent is a substance that reduces another substance by:
In the process of reducing another substance, the reducing agent itself becomes oxidised.
Common Reducing Agents are:
Test for Oxidising Agent: Use of a Reducing Agent e.g. aqueous potassium iodide, KI(aq) Observation: Colourless solution turns brown.
Chemistry behind it: 2I–(aq) => I2(aq) + 2e–
******************************************************************************************************
An oxidising agent is a substance that oxidises another substance by
In the process of oxidising another substance, the oxidising agent itself becomes reduced
Common Oxidising Agents are:
Test for Reducing Agent: Use of an Oxidising Agent e.g. acidified potassium manganate (VII). Observation: Purple solution decolourises.
Chemistry behind it: MnO4–(aq) + 8H+(aq) + 5e– => Mn2+(aq) + 4H2O(l)
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EXERCISE 20(B)
10. A solid cone of height 8 cm and base radius
6 cm is melted and recast into identical cones,
each of height 2 cm and diameter 1 cm. Find
the number of cones formed.
11. The total surface area of a right circular cone of slant height 13 cm is 90 pi cm2.
Calculate :
i) its radius in cm.
(ii) its volume in cm3. [Take = 3-14] .
13. A vessel, in the form of an inverted cone, is
filled with water to the brim. Its height is
32 cm and diameter of the base is 25-2 cm.
Six equal solid cones are dropped in it, s
that they are fully submerged. As a result,
one-fourth of water in the original cone
overflows. What is the volume of each of the
solid cones submerged ?
'14 The volume of a conical tent is 1232 M3 and
the area of the base floor is 154 m2. Calculate
the
(i) radius of the floor,
(ii) height of the tent,
(iii) length of the canvas required to cover this conical tent if its width is 2 m.
EXERCISE 20 D
10. A solid metallic cone, with radius
6 cm and height 10 cm, is made of
some heavy metal A. In order to
reduce its weight, a conical hole is
made in the cone as shown and it
is completely filled with a lighter metal. THE
conical hole has a diameter of 6 cm and depth
cm. Calculate the ratio of the volume of metal
A to THE volume of the metal B in the solid.
EXERCISE 20(E)
3. From a rectangular solid of metal 42 cm by
30 cm by 20 cm, a conical cavity of diameter
14 cm and depth 24 cm is drilled out. Find :
(1) the surface area of remaining solid,
(ii) the volume of remaining solid,
(iii) the weight of the material drilled out
weighs 7 gm per cm^3.
EXERCISE 20(F)
4. A circus tent is cylindrical to a height of 8 m
surmounted by a conical part. If total height
of the tent is 13 m and the diameter of its base
is 24 m; calculate
i) total surface area of the tent,8.
(ii) area of canvas, required to make this tent
allowing 10% of the canvas used for folds
and stitching.
7. A wooden toy is in the shape of
a cone mounted on a cylinder as
shown alongside.
If the height of the cone is 24 cm,
the total height of the toy is 60 cm
and the radius of the base of the
cone = twice the radius of the base of the cylinder
= 10 cm: find the total surface area of the toy.
[Take pi= 3-14]
13. An open cylindrical vessel of internal diameter
cm and height 8 cm stands on a horizontal
table. Inside this is placed a solid metallic right
circular cone. the diameter of whose base is
cm and height 8 cm. Find the volume of
water required to fill the vessel.
If this cone is replaced by another cone,
whose height is 1 3/4 cm and the radius of whose
base is 2 cm, find the drop in the water level.
EXERCISE 20(F)
7. An iron pole consisting of a cylindrical portion
110 cm high and of base diameter 12 cm is
surmounted by a cone 9 cm high. Find
the mass of the pole, given that 1 cm^3 of iron
has 8 gm of mass (approx). (Take pi=355/113)
10. A cylindrical water tank of diameter 2.8 m and
height 4.2 m is being fed by a pipe of
diameter 7 cm through which water flows at
the rate of 4 m/s . Calculate, in minutes, the
time it takes to fill the tank.
11. Water flows, at 9 km per hour, through a
cylindrical pipe of cross-sectional area 25 cm^2.
If this water is collected into a rectangular
cistern of dimensions 7.5 m by 5 m by 4 m;
calculate the rise in level in the cistern in
1 hour 15 minutes.
15. An exhibition tent is in the form of a cylinder surmounted by a cone.
The height of the tent
surmounted by a cone. The height of the tent
above the ground is 85 m and height of the
cylindrical part is 50 m. If the diameter of the
base is 168 m, find the quantity of canvas
base is 168 m, find the quantity of canvas
required to make the tent. Allow 20% extra for
fold and for stitching. Give your answer to the
nearest m^2. [2001]
20. A conical tent is to accomodate 77 persons.
Each person must have 16m^3 of air to
breathe. Given the radius of th ent as 7 m,
is total find the height of the tent and also its curved
surface area.
1 Ahmad throws a dice. Find the probability that it is: a a 2
b not a
c not a 5
d not a multiple of 3.
2 Maha writes the letters of the word 'MATHEMATICS' on separate cards.
She takes one card at random. Find the probability that the letter on the card is: a an M
b not an M
c S or T
d B e before J in the alphabet.
3 In the game of 'Scrabble' there are 100 tiles. Each has one letter or a blank.
The table shows the numbers of tiles with vowels.
One tile is taken at random. Find the probability that it is:
a A
b U
c not O
d a vowel
e not a vowel.
4 Harsha chooses a number at random from this grid. Find the probability that the number she chooses is: a 27
b in the bottom row c in the first column
d not in the last two columns.
Harsha chooses another number at random from the Find the probability that her number is: e less than 10
f more than 10 g not 10
h more than 20.
5 This is a calendar for April in one year.
Anders chooses a day at random. Find the probability that the day he chooses is:
a a Monday b not a Monday c 16 April
d not 16 April
e a Thursday or a Friday.
6 Zalika chooses one day of the year 2015 at random.
a What is the probability that it is: i 5 August ii not 5 August iii in August iv not in August?
b Suppose she chose a day in 2016 instead of 2015. Which probabilities in part a would be greater
now?
7 A computer generates a single-digit random number. It could be any number from 0 to 9.
Find the probability that it is:
a 0 b not 0 c a multiple of 3 d 3.5 e less than 7.
8 A computer generates a two-digit number random number. It can be any number from 00 to 99.
Find the probability that it:
a is 99 b is not 99 c has no 9s in it d has at least one 9 in it.
9 When Razi throws two coins there are four equally likely outcomes.
H = head
T = tail
a How many of these four outcomes will give:
i two heads ii one head and one tail iii two tails?
b If two coins are thrown, what is the probability of getting:
i two heads ii one head and one tail iii two tails?
10 Sasha tosses three coins together.
a Explain why there are eight equally likely outcomes.
b Find the probability that there will be:
i three heads ii three tails iii two heads and one tail iv two tails and one head.
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2. On what sum of money does the S.I. for 10 years at 5% become RS. 1,600 ?
5. In how many years will RS.870 amount to RS.1,044, the rate of interest being 2-1/2% p.a. ?
9. In 4 years, RS.6,000 amounts to RS.8,000. In what time will RS.525 amount to RS.700 at the same rate ?
11. What sum of money lent out at 5% for 3 years will produce the same Interest as RS.900 lent out at 4% for 5 years ?
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