class 10 ex 6.1

Ex 6.1 9:36 PM

Monday, July 6, 2020

Area of circle=

CSA of cylinder=

TSA of cylinder =

Volume of cylinder =

if cylinder is cut from between parallel to height then new surface is produce

TSA of half cylinder = =

if metal solid is melt volume remain same

if water is poured then volume remain same

Book page 82 1a) find the curve surface area , total surface area , volume of following
cylinder

Solution :
Radius( r )= 7
Height (h)=10
we have
CSA of cylinder=

total surface of cylinder =

Volume of cylinder( V)=
4a) The volume of the cylindrical tank is 1.54 liters. If area of base is 77 cm2 find the height of
the cylinder
solution:
volume of the cylinder ( V)=
Area of base(
we have
V=
1540=77

5a) the cylindrical vessel of diameter 1. 4 m hold the water 770 liters find the height of the
cylinder

mensuration Page 1

cylinder
solution:
radius of the cylinder(r ) =
Volume of the cylinder ( v)=

We have
V=
770000=

6a) height and radius of the cylindrical wood are equal . Curved surface area is 308 . find the
height of the wood.
solution:
Height and radius of the cylindrical wood are equal

CSA of cylinder=
308=

h=

7a) the volume of circular cylinder is 539 . If the circumference is 22 find the height of the
cylinder
solution:
circumference ( c )=

22=
volume of the cylinder ( v)

539=
h=
8 a) the circumference of the base of a cylinder is 2.2 ma and height 40 cm find the area
of the total surface area
solution:
Circumference ( c )=

r= 3.5
h=40

TSA of the cylinder =
=

9a) The radius and height of the cylinder are in the ratio of 5: 7 . If the volume of the

mensuration Page 2

9a) The radius and height of the cylinder are in the ratio of 5: 7 . If the volume of the
cylinder is 550 . Find the radius of the base of the cylinder
solution:
ratio of radius and height of cylinder = 5:7

r=5x h=7x

550=
550=22
x= 1
Radius of the cylinder (r )= 5

10 a) the volume of a cylinder is half of its total surface area . If the radius of its base is 7 cm
find its volume.
solution :
Radius ( r ) =7
the volume of a cylinder is half of its total surface area
Volume of cylinder= TSA of cylinder

7h= 7+h
6h=7

Volume of cylinder
=

11) The area of the curved surface of a solid cylinder is equal to the total area of the
same cylinder . If the total surface area is 924 . Find the radius of the cylinder
solution:
curved surface area of a solid cylinder is equal to the total area of the same cylinder
So, CSA of cylinder=

mensuration Page 3

we have ,
TAS of cylinder =

924 =

12) The curved surface area of a cylinder with height equal to the radius of the base is
1232 . Find the total surface area of the cylinder .
Solution:
height equal to the radius
So, r=h
CSA of cylinder=1232

r=14
so, r=h=14

total surface area of the cylinder =

13) the area of the curved surface of a solid cylinder twice the area base and sum of radius
and height is 28 cm . Find the volume of the cylinder .

solution :
sum of radius and height of cylinder =28
so,
Volume of cylinder =?
the area of the curved surface of a solid cylinder twice the area base
CSA of cylinder

h=r
putting value of h in equation (i)

volume of the cylinder= =264
14)
Solution : CSA of cylinder(

volume of cylinder =924

r=
d=

mensuration Page 4

h=

15) A cylindrical bucket with
solution :
volume of cylinder =
water is poured from cylinder to rectangular tank
volume of cylinder = volume of tank

h=
16) The sum of the height and radius of a cylinder is 32 . If total surface area is 1408, find
the volume and the circumference of the base of the cylinder
solution :
r+h=32

TSA of cylinder = 1048

r=7
from …i
h=25
circumference ( C )=
volume (V) =
17) the volume of a cylinder having height twice the radius is 1724 .What minimum
square cm of paper is needed to cover the curved surface area of the cylinders.
solution :
h=2r
volume of cylinder (v)= 1724

r=
h=
we have
CSA=

18) the area of a base of a cylinder is 308 m2 and its volume 1540 m3 find the circumference
of base of cylinder and curved surface of a cylinder
solution :
Area of base (

mensuration Page 5

Area of base (

volume of cylinder (V) =
or 1540=308
circumference ( c) =

CSA of cylinder=
19) if the sum of radius and height of a cylinder is 21 and curved surface area 616 find the
total surface area of cylinder
solution :
r+h= 21
CSA= 616
we have
CSA of cylinder=
616=

total surface of cylinder =

20) Calculate the plane surfaces and total surface area of cylinder having the curved surface
area are 1848 and sum of radius and height 35 cm .
Solution :
r+h=35
CSA of cylinder =
1848=

Area of plane surface area= 2(

total surface of cylinder =

21) find the total surface area solid and ratio of radius and height having the difference
between height and radius 14 and sum 42
solution
r-h= 14
r+h= 42
on solving we get
r=28
h=14
total surface of cylinder =

mensuration Page 6

total surface of cylinder =
22) A cylinder has radius of radius and height in the ratio of 1:3 and their sum 56 . Find its

curve surface area and total surface area
solution :
Ratio of radius and height = 1:3
r=x and h= 3x
Sum of radius is 56
x+3x=56
x=14
r= 14, h=42
CSA of cylinder=

total surface of cylinder =

23) two cylinder have to made from paper having length and breadth 21 cm and 14 cm
respectively by taking base as length and breath . Which cylinder have more volume?
solution
if 21 is as circumference then height is 14
C=
21=
Volume of cylinder( V)=

=

if 14 is as circumference then height is 21

mensuration Page 7