KRISHNA PUBLIC SCHOOL INTERNATIONAL
NAYA RAIPUR
Class – x
Subject – Maths
Assignment – III 2016-17
Topic- Surface Area and Volume
Q.1 A container is in the form of frustum of a cone of height 30 cm with radii of its
lower and upper ends as 10 cm and 20 cm. Find the capacity and S.A of container.
Also find the cost of milk which can completely Fill the container. at the rate of
Rs. 25 per liter.
Q.2 A canal is 300 cm wide and 120 cm deep. The water in canal is flowing with a
speed of 20 km/h. How much area will it irrigate in 20 min if 8 cm of standing
water is desired.
Q.3 A solid toy is in the form of hemisphere surmounted by a right circular cone. The
height of cone is 6 cm and the diameter of base is 10 cm. find volume of the toy. If
a right circular cylinder circums cribes the toy then what is the difference between
the volume of cylinder and the toy.
Q.4 A container shaped like a right circular cylinder has a diameter 12 cm and height
15 cm, is full of icecreame. The icecreame is to be filled into 10 equal cones
having hemispheical shape on the top. If the height of cone is 4 times its radius
then find height of cone.
Q.5 The height of cone is 30 cm. A small cone is cut-off at the top by. a plane parallel
to the base. If its volume is
Q.6
Q.7
Q.8
Q.9
Q.10
Q.11
1
27
th of the volume of cone , at what height above the
base is section made ?
From a solid cylinder whose height is 12 cm and diameter 10 cm. conical cavity
of cone of same height and same diameter is hollowed out. find volume and total
surface Area of solid.
A tent is in the shape of cylinder surmounted by a conical tap. If the height
anddiameter of cylindrical part are2.1 m and 4 m, and slant height of tap is 2.8 m.
find area of Canvas used to make, the tent, also find the cost of canvas at the rate
of 500 per m2.
metallic spheres of radii 6 cm, 8 cm and 10cm respectively are melted and recast
into a single solid sphere. find the surface area of solid sphere formed.
A decorative block is made of two solids a cube and a hemisphere. The base of
block is the cube with edge of 5 cm and and hemisphere attached on the top has
diameter 4.2 cm. find Total area to be painted.
A shuttle cock used for badminton has the shape of frusfum of a cone mounted on
a hemi sphere. The external diameters of the frustum are 6 cm and 2 cm and the
height of entire shuttle cock is 7 cm find its external surface Area.
A hollow cylinder has solid hemisphere inward at one end and on the other end it
Q.12
Q.13
Q.14
Q.15
Q.16
Q.17
Q.18
Q.19
is closed with a flat circular plate. The height of water is 10 cm when flat circular
Surface is downward find level of water when it is inverted upside down, com
mon diameter is 7 cm, and height of cylinder is 20 cm.
from a rectangular solid of metal 42 cm by 30 cm by 20cm, a conical cavity of
diameter 14 cm and depth 24 cm is drilled out. find(a) The surface area of remaining solid.
(b) The volume of remaining solid.
(c) The weight of material drilled out, it it weight 7 gm per cm3
From a solid cylinder whose height is 16 cm and radius 12 cm aconical cavity of
height 8 cm and base radius 6 cm is hollowed out. find volume and total S.A of the
solid.
A petrol tank is a cylinder of base diameter 21 cm and length 18 cm fitted with
conical ends each of axis length 9 cm Determine the capaeity of tank.
A hollow sphere of internal and external radii 6 cm and 8 cm respectively and
recast into small cones of base radius 2 cm and height 8 cm. find the No. of
cones.
A spherical glass vessel has a cylindrical ncck 8 cm long. 2 cm in diameter and
diameter of spherical part is 8.5 cm. By measuring the amount of water is holds a
girl finds its volume to 345 cm3 check whether she is correct taking the above
inside measure ments.
A vessel is in the form of inverted cone. It’s height is 8 cm and radius of its top
which is open, is 5 cm. If is filled with water up to brim. when lead shots each of
which is a sphere of radius 0.5 cm are dropped in vessel, one fourth of water
flows out. find No. of shots dropped in vessel, 1/4 of water flows out. find
No. of shots dropeped in vessel.
from a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a camical
covity of the, same height and same diameter is hollowed out. find T.S.A of remaining solid.
mayank made a birdbath for his garden in the shape of conical with a hemispheri
cal depression at one end as shown in fiq. The height of hollow cylinder is 1.45 m
and radius is 30 cm. find Total suface Area of bird bath.
Q.20 A metal container in the form of cylinder is surmounted by a hemisphere of the
same radius. The internal height of the ylinder is 7 m and the internal radius is 3.5
m. Calculate.
(a) The Tatal area of internal surface excluding the base
(b) The internal volume of the container in m3.
Q.21 Mohit and his wife Poonam are busy for making Jaggery out of sugarcane juice.
They have processed the sugarcane juice to make the molasses, which is poored
into moulds in the shapes of frustum of cone having diameter of its two circular
faces and vertical height of 14cm. If each cubic cm of molasses has mass about
1.2gm. Find mass of molasses that can be poored into each mould.
Q.22 A test tube consist of hemisphere and a cylinder of same radius. The volume of the
water regnuired to fill the whole tabe is
Q.23
Q.24
Q.25
Q.26
Q.27
Q.28
Q.29
Q.30
4235
5159
3 and
3
cm
6 cm
6
of water is required
to fill the tube to a level which is 4 cm below the top of the tabe. find radius of
tube and length of cylindrical part.
A cone of height 24 cm and radius of base 6 cm is made up of modelling day. A
child reshapes is in the form of sphere find radius of cylinder.
A copper wire 3 mm in diameter is wound around a cylinder whose length is 1.2
and diameter 10 cm so as to cover the curved S.A of cylinder. find length and
mass of wire assuming that the density of wire to be 8.88 gm/cm3
A hemispherical bowl of internal radius 9 cm is full of liquid . The liquid is to be
filled into cylindrical shaped small bottles each of diameter 3 cm and heiqht 4 cm
. How many boltles are needed to empty the bowl ? Also find S.A of hemispheri
cal bowl.
If the diameter of the Cross section of a wire is decreased by 5%.then how much
percent will the length be incrcase so the volume remain same.
A wooden artical was made by scooping out a hemisphere from each end of a
solid cylinder. If the height of the cylinder is 3.5 cm find the total S.A of article
A room is 8 m long, 4.5 m wide and 2.8 high. It has One door 1.4 m wide and 2 m
high with a semicirular ventilator as shown in the given fiq. and two rect angular
windows 2 m by 15 m each. Find the cost of white washing the inner four walls
of the room at the rate of 10 per m2.
A bucket is in the form of a frustam and holds 28, 490 L of water. The radii of the
top and bottom are 28 cm and 21 cm respectively. find heiqht of bucket.
A rectangular sheet of of paper 22 cm long and 12 cm wide. A cylinder is formed
by rolling the paper along length find vol. of cylinder.
KRISHNA PUBLIC SCHOOL INTERNATIONAL
NAYA RAIPUR
Class – x
Subject – Maths
Assessment – III 2016-17
Topic : Area Related to Circle
Q.1 In a circle of radius 10 cm, an arc subtends an angle of 900 at the centre. Find area
of major sector.
Q.2 A paper is in the form of rectangle ABCD in which AB=16 cm and BC=12 cm. A
semicircle portion with BC as diameter is cut-off. Find out area of remaining
solid.
Q.3 A round table cover has six equal designs as shown in figure. If the radius of
cover is 28 cm then find cost of making design at the rate of 0.35 per m2.
Q.4 Two concentric circles are of radii 15cm and 3cm. Find the length of chord of the
larger circle which touches the smaller circle.
Q.5 A chord of a circle of radius 12cm subtends an angle of 1200 at the centre. find the
area of corrosponding segment of the circle.
Q.6 A chord of a circle of radius 10cm subtends a right angle at the centre. find the
area of CorrospondingA
minor segment
b
majar seetor.
Q.7 On a square hand kerchief, 9 circular design each of radius 7 cm are made find
the area of remaining portion of hand kerchief.
Q.8 In the given figure o is the centre of a circle with radius 14 cm. AOB and COD are
two perpendicular diameters of the circle. find the area of shaded region.