CBSE Important Mathematics Questions of Class X Chapter {Surface Area and Volume} for CBSE Examination 2023
1)
Three solid metallic
spherical balls of radius 3 cm, 4 cm and 5 cm are melted into a single
spherical ball, find its radius.
2)
The curved surface area of a
cylinder is 264 m2 and its volume is 924 m3. Find the ratio of its
height to its diameter.
3)
If the radius of the base of
the right circular cylinder is halved, keeping the height same, then find the
ratio of the volume of the cylinder does obtain to the volume of the original
cylinder.
4)
Find the volume of the
largest right circular cone that can be cut out from a cube of Edge 4.2 CM.
5)
Find the curved surface area
of a right circular cone of height 15 cm and base diameter 16 cm.
6)
Volume of two spheres one in
the ratio 64: 27. What will be the ratio of their surface areas?
7)
A metal cube of Edge 1 cm is
drawn into a wire of diameter 4 mm, then find the length of the wire.
8)
Find the total surface area
of a solid hemisphere of radius 7cm.
9)
A solid iron in the form of a
cuboid of dimensions 49 CM X 33 CM X 24 cm is melted to form a solid
sphere. Find the radius of sphere.
10) Total surface area of a cube is 216 CM2, find its volume.
11) The radii of two cylinders are in the ratio of 2:3 and
their heights are in the ratio 5:3. Find the ratio of their volumes.
12) Find the ratio of volumes of a cone and cylinder of equal
diameter and equal height.
13) Find the curved surface area of a right circular cone of
height 15 cm and base diameter 16 cm.
14) If the radius of circular ends of a frustum of a cone are
20 cm and 12 cm and its height is 6 CM, then find the slant height of frustum.
15) If a solid right circular cone of height 24 cm and base
radius 6 cm is melted and recast in the shape of a sphere, then find the radius
of the sphere.
16) A solid sphere radius r is melted and recast into the shape
of a solid cone of height r, then find the radius of the base of the cone.
17) If a cone is cut into two parts by a horizontal plane
passing through the midpoint of its axis, find the ratio of the volumes of the
upper part and the cone.
18) A shuttlecock used for playing badminton combination of two
geometric shapes. Name the two geometrical shapes.
19) Find the volume of the largest square that can be cut from
cylindrical log of wood of base radius 1 m and height 4 cm.
20) Find the number of plates of diameter 1.5 cm and 0.2 CM
thick each, that can be fitted completely inside a right circular cylinder of
height 10 cm and diameter 4.5 CM.
21) A cone of height 24cm and radius of base 6 cm is made up of
clay. If we reshapes it into a sphere, find the radius of the sphere.
22) A 5 m wide cloth is used to make a conical tent of base
diameter 14m and height 24m. find the cost of cloth used at the rate of Rs 25
per m.
23) If the total surface
area of a solid hemisphere is 462 CM2, find its volume.
24) A solid metallic
sphere of diameter 8 m is melted and drawn into a cylindrical wire of uniform
width. if the length of the wire is 12 m find its width.
25) Find the number of spherical bullets of radius 1 mm each
that can be made out of a cylindrical solid of radius 4 cm and height 6 CM.
26) A cubical block of side 7 cm is surmounted by a hemisphere.
What is the greatest diameter the hemisphere can have? Find the surface area of
the solid.
27) A solid is in the shape of a cone surmounted on a
hemisphere, the radius of each of them being 3.5 cm and the total height of
solid is 9.5 CM. Find the volume of the solid.
28) A cylinder and a cone have base radius 5cm and 3cm
respectively and their respective Heights are 4cm and 8cm. find the ratio of
their volumes.
29) A glass cylinder with diameter 20 CM has water to a height
of 9 CM. A metal cube of 8 cm edge is immersed in it completely. Calculate the
height by which water will rise in the cylinder.
30) A metallic solid sphere of radius 4.2 cm is melted and
recast into the shape of a solid cylinder of radius 6 CM. Find the height of
the cylinder.
31) From a solid cylinder whose height is 2.5 cm and diameter
1.4 CM a conical cavity of the same height and same diameter is hollowed out.
Find the volume of the remaining solid to the nearest cm3.
32) A metallic sphere of total volume π is melted and recast
into the shape of a right circular cylinder of radius 0.5 CM. What is the
height of cylinder?
33) A sphere of maximum volume is cut out from a solid
hemisphere of radius 6 CM. find the volume of the cut out sphere.
34) 50 circular plates each of radius 7 cm and thickness 0.5 CM
are placed one above another to form a solid right circular cylinder. Find the
total surface area and volume of the cylinder so formed.
35) A semicircular sheet of paper diameter 28cm is bent into
an open conical cup. Find the depth and capacity of the cup.
36) A solid cuboid of iron of dimensions 66 cm X 20 cm X 27 cm is used to cast an iron pipe. if the
outer diameter of the pipe is 10 cm and thickness is 1 cm, then calculate the
length of the pipe.
37) A hemispherical bowl of internal diameter 36 cm contains
liquid. this liquid is to be filled into cylindrical shaped Bottles of radius 3
cm and height 6 CM. how many bottles are required to empty the bowl?
38) Solid spheres of diameter 6 CM are dropped into a
cylindrical beaker containing some water and are fully submerged. if the
diameter of the beaker is 18 cm and the water rises by 40 cm in the
beaker, find the number of solid spheres dropped in the water.
39) The diameter of a metallic solid sphere is 9cm. It is
melted and drawn into a wire having diameter of cross section as 0.2 cm. Find
the length of the wire.
40) Wax cylinder of diameter 21 cm and height 21 cm is chipped
off and saved to form a cone of maximum volume. The chipped of wax is recast
into a solid sphere. Find the diameter of the sphere.
41) 4 cubes of volume 125 cm3 each are joined end to
end in a row. Find the surface area and volume of the resulting cuboid.
42) A cubical solid block of metallic 49 cm X 44 cm X 18 cm is
melted and formed into a solid sphere, calculate the radius of the sphere.
43) A well of diameter 4m is dug 21m deep. the earth taken out
of it has been spread evenly all around it in the shape of a circular ring of
width 3m to form an embankment. Find the height of the embankment.
44) The sum of the radius of base and height of a solid right
circular cylinder is 37 CM. If the total surface area of the solid cylinder is
1628 sq. cm. Find the volume of the cylinder.
45) A right circular cone of radius 3 cm has a curved surface
area of 47.1 CM2. Find the volume of the cone.
46) A toy is in the form of a cone of base radius 3.5 CM
mounted on a hemisphere of base diameter 7 cm. if the total height of the toy
is 15.5 CM, find the total surface area of the toy.
47) A tent is in the
shape of a cylinder surmounted by a conical top of same diameter. If the height
and diameter of cylindrical part are 2.1 and 3m respectively and the slant
height of conical part is 2.8m, find the cost of Canvas needed to make the tent
if the Canvas is available at the rate of RS. 500 per square metre.
48) A conical vessel with base radius 5 cm and height 24cm is
full of water. This water is emptied into a cylindrical vessel of base radius
10 cm. Find the height to which the water will rise in the cylindrical vessel.
49) A sphere of diameter 12 cm is dropped into a right circular
cylindrical vessel, partly filled with water. If the sphere is completely
submerged in water, the water level in the cylindrical vessel Rises by 32 /9
cm find the diameter of the cylinder vessel.
50) A hemispherical tank of diameter 3M is full of water. it is
being emptied by a pipe at the rate of 25/7 litre per second. How much time
will it take to make the tank half empty.
51) A cylindrical tub whose diameter is 12 cm and height 15 CM
is full of ice cream. The whole ice cream is to be divided into 10 children in
equal ice cream cones with conical base surmounted by a hemispherical top. If
the height of conical portion is twice the diameter of base, find the diameter
of conical part of ice cream cone.
52) A metal container open from the top is in the shape of a
frustum of a cone of height 21cm with radius of its lower and upper circular
ends is 8 cm and 20 CM respectively. Find the cost of milk which can completely
fill the container at the rate of Rs. 35 per litre.
53) A cylindrical glass tube with radius 10 cm has water up to
a height of 9 CM. a metal cube of 8 cm edge is immersed completely. By how much
the water level will rise in the glass tube?
54) From a solid cylinder whose height is 2.4 cm and diameter
1.4 CM, a conical cavity of the same height and same diameter is hollowed out. Find
the total surface area of the remaining solid to the nearest cm2.
55) A girl empties a cylindrical bucket full of sand of base
radius 18 cm and height 32 CM on the floor to form a conical heap of sand. if
the height of this conical heap is 24 cm, then find its slant height correct up
to one place of decimal.
56) The largest possible sphere is carved out of wooden solid
cube of side 7 cm. find the volume of wood left.
57) A wooden toy was made by scooping out a hemisphere of same
radius from each end of the solid cylinder. If the height of the cylinder is 10
cm and its base is of radius 3.5 cm, find the volume of word in the toy.
58) A bucket is in the form of a frustum of a cone and it can
hold 28.49 litre of water. if the radius of its circular ends at 28 cm and 21
CM, find the height of the bucket.
59) A hemisphere bowl of internal radius 9 cm is full of water.
Its contents are emptied in a cylindrical vessel of internal radius 6 CM. find
the height of water in the cylindrical vessel.
60) Two cubes each of volume 64 CM3 are joined end to end. Find
the surface area of the resulting cuboid.
61) A vessel is in the form of a hollow hemisphere mounted by a
hollow cylinder. The diameter of the hemisphere is 14 cm and the total height
of The vessel is 13 cm. Find the inner surface area of the vessel.
62) A cubical block of side 7 cm is surmounted by a hemisphere.
What is the greatest diameter of the hemisphere can have? Find the surface area
of the solid.
63) A medicine capsule is in the shape of a cylinder two
hemispheres stuck to each of its ends. The length of the entire capsule is 14
mm and the diameter of the capsule is 5 mm. Find its surface area.
64) From a solid cylinder whose height is 2.4 cm and diameter
1.4 cm, a conical cavity of the same height and same diameter is hollowed out.
Find the total surface area of the remaining solid to the nearest cm2.
65) A solid is in the shape of a cone standing on a hemisphere
with both their radius being equal to 1 cm and the height of the cone is equal
to its radius. Find the volume of the solid in term of π.
66) A solid iron pole consists of a cylinder of height 220 cm
and base diameter 24 cm which is surmounted by another cylinder of height 60cm
and radius 8 cm. find the mass of the pole given that one cm3 of iron has
approximately 8 gram mass.
67) A metallic sphere of radius 4.2 cm is melted and recast
into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
68) A metallic spheres of radii 6 cm, 8 cm and 10 cm
respectively are melted to form a single solid sphere. Find the radius of the
resulting sphere.
69) A cylindrical bucket 32cm 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 then find the radius
and slant height of the heap.
70) A fez, used by turks is shaped like the frustum of a cone.
if it's radius on the open side is 10 cm radius at the upper base is 4 cm and
its slant height is 15 CM then find the area of material used for making it.
71) A metallic right circular cone 20cm high and whose Vertical
angle is 60 degree is cut into two parts at the middle of its height by a plane
parallel to its base. if the frustum so obtained be drawn into a wire of
diameter 1/16 cm then find the length
of the wire.
72) A hemispherical depression is cut from one face of a
cubical block such that diameter of hemisphere is equal to the edge of cube.
find the surface area of the remaining solid.
73) A container open at the top is in the form of a frustum of
a cone of height 24cm with radius of its lower and upper ends as 8 cm and 20 CM
respectively find the cost of milk which can completely fill the rate of Rs. 21
per litre.
74) A metallic bucket open at the top of height 24cm is in the
form of frustum of a cone the radius of whose lower and upper ends are 7 cm and
14 cm respectively. Find the volume of water that can fill the bucket and area
of metal sheets.
75) A cone is cut by a plane parallel to the base and upper
part is removed if the curved surface area of the remainder is 15 /16 of the
curved surface area of whole cone, find the ratio of the line segment to which
the cones height is divided by the plane.
76) Water in a Canal 6M wide and 1.5 m deep is flowing with the
speed of 10 km per hour. How much area in hectare will it irrigate in 30
minutes is 8 cm of standing water is needed?
77) A farmer connects a pipe of internal diameter 20 cm from a
Canal into a cylindrical tank in his field, which is 10 m in diameter and 2m
deep. if water flows through the pipe at the rate of 3 km per hour In how much
time will the tank be filled.
78) Water is flowing
through a cylindrical pipe of internal diameter 2 cm, into a cylindrical tank
of base radius 40 cm, at the rate of 0.4 M per second. Determine the Rise in
level of water in the tank in half an hour.
79) A Military tent of height 8.25 m is in the form of a right
circular cylinder of base diameter 30 M and height 5.5 m surmounted by a right
circular cone of same base radius. Find the length of the Canvas used in making
the tent if the breadth of the Canvas is 1.5m.
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