Revision Questions
for class IX
1)
Find the length of the longest iron rod
that can be placed in a room 30 m long, 24 m broad and 12 .2 m high.
2)
The lateral surface area of a right
circular cylinder of height 12 cm is1848 cm2. Find the volume of the
cylinder.
3)
A mansion has 12 cylindrical pillars each
having radius 50 cm and height 3.5 m. Find the cost to paint the curved surface
of the pillars at Rs. 20 per square meter.
4)
Ramesh threw a party on the recovery of
his injured friend from the accident. Ramesh served him and other friends
with chilled juice which was in cylindrically shaped cans of radius 4.2 cm and
height 15 cm. Find the total volume of juice they drink and total surface area
of 7 juice cans. Which value is depicted by Ramesh ?
5)
A cubicle water tank is filled by tap
water at the rate of 1.4 litres per second. Find the length of an edge of the
tank in centimeters if the tank is completely filled in 28 minutes.
6)
A closed wooden box has outer dimensions
as 10 cm by 8 cm by7 cm. The thickness of wood is 1cm. If 1 cm3 of
wood costs Rs 2, find the total cost of the wood required to make the box.
7)
If the total surface area of the sphere
is 5544 cm2, find the diameter of the sphere.
8)
A hemispherical bowl is made of steel
0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved
surface area of the bowl.
9)
The patients in a hospital are given soup
daily in a cylindrical bowl of diameter 21 cm. On a particular day, the girl
decided to cook the soup for patients. If they fill the bowl with soup to a height
of 7 cm.
10) A corn cob, shaped somewhat like a cone
has the diameter of its broadest end as 4cm and length as 20 cm. If each 1 cm2
of the surface of the cob carries an average of three grains, find how
many grains you would find on the entire cob
11) A heap of wheat is in the form of a cone
whose diameter is 10.5 m and height is 3 m. Find its volume. If cost of 1 m3
wheat is Rs.10 then find total cost. Also find slant height of heap.
12) ABC is an isosceles triangle with each
equal side 5 cm, perimeter 18 cm and height AD = 7 cm. Then,
find the area of the triangle ABC
13) The area of a triangle is equal to the
area of a rectangle whose length and breadth are 18 cm and 12 cm
respectively. If the base of the triangle is 24 cm, then find its
altitude
14) PQRS is a trapezium with
PQ||SR. A line parallel to PR intersects PQ at L and QR at M. Prove that ar
(ΔPSL) = ar (ΔPRM).
15) In the figure, ABCD is a
parallelogram and BC is produced to a point Q such that AD =
CQ. If AQ intersects DC at P, show that ar
(BPC) = ar (DPQ)
16) Prove that parallelograms on
the same base and between the same parallels are equal in area.
17) ABCD is a trapezium with
AB||DC. A line parallel to AC intersects AB at X and BC at Y. Prove
that ar (ADX) = ar (ACY).
18) Diagonals of a parallelogram
ABCD intersect at point O. Thourgh O, a line is drawn to intersect AD at P and
BC at Q. Show that PQ divides the parallelogram into two parts of equal area.
19) Diagonals PR and QS of
quadrilateral PQRS intersect at T such that
PT =TR. If PS = QR, Show that ar (ΔPTS) = ar (ΔRTQ).
20) Diagonal AC and BD of a
quadrilateral ABCD intersect at O in such a way that ar (AOD)= ar (BOC). Prove that ABCD is a
trapezium.
21) PQRS and ABRS are
parallelograms and X is any point on side BR. Show that :
i)
area PQRS = area ABRS
ii)
area AXS = ½ area
PQRS.
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