If a sphere is placed inside a right circular cylinder so as to touch the top, base and the lateral surface of the cylinder. If the radius of the sphere is R, the volume of the cylinder is

M4maths Previous Puzzles

02 Sep 2015 Volume If a sphere is placed inside a right circular cylinder so as to touch the top, base and the lateral surface of the cylinder. If the radius of the sphere is R, the volume of the cylinder is: OPtion
1) 4 Pi R^3
2) 6 Pi R^3
3) 5/2 Pi R^3
4) 8/3 Pi R^3
5) 12 Pi R^3
6) 2 Pi R^3
7) 7/3 Pi R^3
8) 8 Pi R^3
9) 10 Pi R^3
10)None of these; Correct Option: 6 Best Solution (73)

ABHINAV PUSHPAM 9 years AGO

Answer is - 2pi r^3
Explanation
H=2R
Volume of cylinder = pi * R^2* H
Put h=2r
so volume will be pi*r^2 * 2r = 2 * pi *r^3

Like? Yes (12) | No

Abhijeet 9 years AGO

radius of cyl = rad of sphere
height of cylinder=diameter of sphere

Like? Yes (4) | No

Ravi Yadav 9 years AGO

from given information
radius of cylinder base=R=r
Height of cylinder=2R=h
volume of cylinder = pi*r^2*h
ANS= 2*pi*R^3.

Like? Yes (2) | No

pravin kumar 9 years AGO

height of cylinder = 2r
therefore volume of cylinder= pi*r*r*h= pi*r*r*2r=2*pi*r*r*r

Like? Yes (2) | No

Anusha Kota 9 years AGO

volume of the right circular cylinder=pi*r*r*h
here h=2*r as per the given conditions.
so volume of cylinder= pi*r*r*2*r
=2*pi*r*r*r

Like? Yes (1) | No

sudiptaa 9 years AGO

Height of cylinder = 2R
Volume of cylinder = Pi * R ^2 * H
= 2*Pi * R^3

Like? Yes (1) | No

ramya 9 years AGO

The volume of the cylinder must be 2Pi r^3 using the volume of sphere and cylinder

Like? Yes (1) | No

Rahul kumar 9 years AGO

VOL OF CYLINDER=PI*R^2*H
here H=2R
so, vol=2PIr^3

Like? Yes (1) | No

Prathyusha 9 years AGO

Radius of Cylinder = R,
Height of Cylinder = 2R,
then, Volume of Cylinder = Pi*R^2*H,
= Pi*R^2*2R
= 2 Pi R^3

Like? Yes (1) | No

siddhi datri 9 years AGO

let the heights be h and radius be r
h=2r
volume=pi r^2h= 2 Pi r^3

Like? Yes (1) | No

surendra 9 years AGO

bcz sphere touches uper lower and lateral surfaces . so height of cylinder is 2r hence volume is pi*r*r*2r=2pir3

Like? Yes (1) | No

ANIK KUMAR HALDER 9 years AGO

as the sphere touches the top and bottom and curved surface area of the cylinder .
so radius of the cylinder =radius of the sphere=R
height of the cylinder=R+R=2R
area of the cylinder =pi*r^2h=pi*R^2*(2R)=2piR^3

Like? Yes (1) | No

tamilmani 9 years AGO

volume=pi r^2 h
r=r
h=2r
volume=pi(r^2)*(2r)
=pi*2(r^3)

Like? Yes (1) | No

Nitheesh Aithu 9 years AGO

let r=radius of base and top of cylinder and h=height of cylinder
According to the problem given,
r=R,h=R+R=2R
where R=Radius of inner placed sphere
Volume of R.C.C=pi*r^2*h=pi*R^2*2R
=2*pi*R^3

Like? Yes (1) | No

praveendas 9 years AGO

volume of the cylinder is pi*r^2*h
h is 2R.
therefore volume is 2*(pi)*R^3

Like? Yes (1) | No

umang agarwal 9 years AGO

here sphere touches both upper nd base of cylinder.
so, diameter of sphere=height of cylinder.=2r.
so the area of cyinder=pi*r^2*h=pi*r^2*2r=2pi*r^3

Like? Yes (1) | No

Prabhat Burnwal 9 years AGO

radius of the cylinder=R
height of the cylinder=2R
volume=2 PI R^3

Like? Yes (1) | No

Sahana Jayasimha 9 years AGO

Given:
a. The radius of the sphere is R
b. The sphere is touching the top,bottom and lateral surfaces of the cylinder .
Therefore from this we can infer that the height of cylinder is equal to the diameter of the sphere , h=2R
and the radius of the cylinder is equal to the radius of the sphere.
volume of cylinder is =PI* (R^2) *h
= PI * (R^2) * 2R
= 2 PI R^3

Like? Yes (1) | No

Monika Nemiwal 9 years AGO

volume of cylinder=Pi*r^2*h
Pi(R^2)(2R)
2Pi(R^3)

Like? Yes (1) | No

Sushant Kumar 9 years AGO

r=R
h=2R
VOLUME OF CYLINDER= PIr^2h
= piR^2*2R
= 2piR^3

Like? Yes (1) | No

RAVAL 9 years AGO

sphere is placed in cylinder
so, height (h) = 2R
volume of cylinder = pi* R^2 * 2R
= 2*pi*R^3

Like? Yes (1) | No

SHIVUMUNI SHASTRIMATH 9 years AGO

volume of sphere=4/3 pi r^3
volume of cylinder=pi r^2 h
substitute sphere volume in cylinder i.e.
pi r^2 h, h=2r so answer is 2 pi r^3

Like? Yes (1) | No

vikas kulshrestha 9 years AGO

the radius of the cylinder = R
height of the cylinder = 2R
volume of cylinder =Pi R^2 (h)
=Pi R^2 (2R)
=2 Pi R^3

Like? Yes (1) | No

Amiya Ranjan 9 years AGO

radius of the sphere is R , so the radius of the bottom circle of the cylinder will be R as well. The height of the cylinder will be equal to the diameter of the sphere so H=2R.

Vol=pi*r^2*h=pi*r^2*2r=2*pi*r^3

Like? Yes (1) | No

Zulekha Parveen 9 years AGO

sphere covers cylinder.
radius of base of cylinder=R
height of cylinder=diameter of sphere=2R
so, vol of cylinder=pi*r^2*h
=pi*R^2*2R
=pi*2R^3

Like? Yes (1) | No

Devendra Marghade 9 years AGO

Cylinder's Radius=R and Height=2R
So Volume of Cylinder=Pi*(Radius)^2*Height
=Pi*R^2*2R=2*Pi*R^3
Option 6)

Like? Yes (1) | No

gaurav 9 years AGO

height=2r
radius=r
apply formula for volume of cylinder

Like? Yes (1) | No

gaurav singh 9 years AGO

radius of sphere=R
height of cylinder=2R
volume of cylinder = pi r^2 h
=> pi R^2 (2R)
=> 2 Pi R^3

Like? Yes (1) | No

PAWAN KUMAR 9 years AGO

RADIUS OF CYLINDER = R , HEIGHT = 2R
SO, VOLUME = 2*PI*R^3.

Like? Yes (1) | No

PIYUSH AGRAWAL 9 years AGO

volume of cylinder is 2 pi r^2 h
but here h = r so

Like? Yes (2) | No (1)

Rishab Kumar 9 years AGO

h=2R
r=R
volume of cylinder=pi*r*r*h
=2*pi*R^3

Like? Yes (1) | No

Goutham Venkatesh K 9 years AGO

radius of cylinder = r
height of cylinder = 2r
volume = pi r^2 h = pi * r * r * 2r = 2 Pi r^3

Like? Yes (1) | No

milan gupta 9 years AGO

r of cylinder =r of sphere
h of cyl.=2xr of sphere

Like? Yes (1) | No

nikhil bansal 9 years AGO

volume of cylinder = pi r^2 h
here r=R
h=2R
so
volume = pi R^2 2R = 2pi R^3

Like? Yes (1) | No

ajay kulkarni 9 years AGO

If R is the radius of the sphere and sphere touches the cylinder internally then
length of cylinder is 2R and radius of cylinder is R
then volume of cylinder is
=pi*R^2*(2R)=2*pi*R^3.

Like? Yes (1) | No

kriti kankariya 9 years AGO

volume of cyl = pi * r^2 *h
here r of cyl=R of sphere
and h of cyl = 2R of sphere
therefore,vol of cyl = pi* R^2 *2R
= 2*pi* R^3

Like? Yes (1) | No

YASWANTH REDDY 9 years AGO

as per the given information, the height of the cylinder is equal to 2 times of radius of the sphere and therefore,
Volume of cylinder = pi R^2 H = pi R^2 * (2R) = 2 pi R^3

Like? Yes (1) | No

Deepanshu Chaturvedi 9 years AGO

Radius of sphere = Radius of cylinder
Height of cylinder = 2 * Radius of sphere
so, volume of cylinder = Pi * (R)^2 * H
= Pi * R^2 * 2 * R
= 2 Pi R^3

Like? Yes (1) | No

Gayathri 9 years AGO

Given radius of the sphere= r
as it touches the base, top and lateral surface, height of the cylinder,h=r+r=2h
volume of the cylinder = pi*r^2*h
replace h with 2r
therefore, volume of the cylinder=pi*r^2*2r
= pi*r^3

Like? Yes (1) | No

Archie 9 years AGO

Volume of cylinder=pi*R^2*h
h=dia. of sphere = 2R
Vol. of cylinder =pi*R^2*(2R)
=2 Pi R^3

Like? Yes (1) | No

vishal varma 9 years AGO

volume of cyinder=pir^2H
PI*R^2*2R=2PIR^3
ssince ht of cylinder= diameter of circle=2r

Like? Yes (1) | No

Dipanjan Bhattacharjee 9 years AGO

The diameter of the circle is 2R which is actually the height of the cylinder

Like? Yes (1) | No

Rishav Kumar 9 years AGO

since, the sphere is touching top ,base and lateral surfaces of the cylinder
hence, height of cylinder=2* radius of sphere
&& radius of cylinder,s base= radius of sphere
v=pi* R^2 * h=pi* R^2 * 2*R =2*pi*R^3

Like? Yes (1) | No

anant rathi 9 years AGO

Radius of cylinder = radius of sphere
Height of cynlinder = 2* R

Like? Yes (1) | No

diksha 9 years AGO

radius of cylinder= r
height = 2r
volume=pi*r^2*h
=pi*r^2*(2r)
=2pir^3

Like? Yes (1) | No

Vertika Srivastava 9 years AGO

radius of sphere=r=radius of cylinder
so, diameter of sphere=2r=height of cylinder
volume of cylindder= pie r^2*h

Like? Yes (1) | No

Rashmi Verma 9 years AGO

volume of cylinder= ?r^2h
h=2r
vol=2?r^3

Like? Yes (1) | No

Pronab Paul 9 years AGO

Vol of cylinder=pi*r^2*h
Here radius of cylinder=radius of sphere=R
And height of cylinder= diameter of sphere=2R
So, vol= pi*R^2*2R=2pi*R^3

Like? Yes (1) | No

raj sekhar 9 years AGO

height of cylinder: 2R
radius of cylinder: R
bol of cylinder: circle area * height
=pi* (R)� * (2R)

Like? Yes (1) | No

rahul raj sharma 9 years AGO

volume of cylinder=pi*r*r*h
and radius of circle is R which is also the radius of cylinder and also height of cylinder is 2R because it is equal to diameter of circle

Like? Yes (1) | No

ishan chourishi 9 years AGO

volume of cylinder is pi *r^2*h
here h=2R (as cylinder is touching all sides so 2*radius =h)
r=R
so pi*r^2*h= pi *R^2* 2R => 2 pi R^3

Like? Yes (1) | No

M.V.S sai sunidhi 9 years AGO

as the sphere is connected to top ,bottom and lateral surfaces ,the height of cylinder is,h=2*r
so as volume of cylinder is ,v=pi*r^2*h=pi*r^2*2*r
=2*pi*r^3

Like? Yes (1) | No

Sivaprakash.J 9 years AGO

Height of sphere is 2R
Then,
Volume of cylindet=πR^2h
Now volume is 2πR^3

Like? Yes (1) | No

Ravi kumar 9 years AGO

Here the radius of sphere will be equal to radius of cylinder and height of the cylinder will be = to diameter of sphere .

Like? Yes (1) | No

suhail anjum 9 years AGO

curved surface area of the sphere placed inside the right circular cylinder is same as cylinder.so base radius of cylinder is same as radius of sphere and hence height is two times of radius of sphere .

Like? Yes (1) | No

Vatan Chaudhary 9 years AGO

volume of cylinder=pie *(R)sq*H
here H= 2R
therefore volume of cylinder=pie*(R)cube

Like? Yes (1) | No

shyam sundar satpathy 9 years AGO

Here radius of cylinder is equal to the radius of sphere i.e. 'R' and height is the diameter of the sphere i.e. '2R' so
volumn of cylinder is =PI * R*2R=2 PI R^3

Like? Yes (1) | No

NAGENDRA P 9 years AGO

volume of a cylinder= pi*r*r*h=pi*R^2*2R=2pi*R^3
so option (6)

Like? Yes (1) | No

Surabhi Yadav 9 years AGO

volume of cylinder=pi r^2 h
sphere touching cylinder= 2R^3 pi
hence option (6)

Like? Yes (1) | No

Ashish Kumar Karan 9 years AGO

height=2*R
volume=(pi*R^2)*(2*R)
=2*pi*R^3

Like? Yes (1) | No

Prateek sanganeria 9 years AGO

as volume of a cyliner = pi*r^2*h
here h=2r
therefore, V=2*pi*R^3

Like? Yes (1) | No

Kishan Kumar 9 years AGO

Height =2R, Radius = R then put iy into volume of cylinder formula

Like? Yes (1) | No

sidd 9 years AGO

height = 2R
radius = R
volume = pi * R^2 * H = 2 * pi * R^3

Like? Yes (1) | No

KAVITHA 9 years AGO

Volume of the cylinder is
Pi*R^2*H
here is is 2R as diameter of the circle which is the height of the cylinder so
Volume is 2*Pi*R^3

Like? Yes (1) | No

Aman Gaurav 9 years AGO

Volume of the cylender is
Pi*R^2*H
here is is 2R as diameter of the circle which is the height of the cylinder so
Volume is 2*Pi*R^3

Like? Yes (1) | No

Aman 9 years AGO

Volume of the cylinder is
Pi*R^2*H
here is is 2 R as diameter of the circle which is the height of the cylinder so
Volume is 2*Pi*R^3

Like? Yes (1) | No

Shubhendu Shrivastava 9 years AGO

volume of regular cylinder= pi*r*r*h
here, the sphere touches the top, base and the lateral surface thence, the cylinder has the diameter of base equal to the height. therefore, h=2R
So, vol= pi*R*R*2R
=2*pi*R^3

Like? Yes (1) | No

Khushboo Pasari 9 years AGO

Volume of a Cylinder= Pi R^2 H
Sphere is in the Right Circular Cylinder with the condition that it touches the top, base and the lateral surface.
Hence, Height of the Cylinder, H= 2 R
Volume of the Cylinder= Pi R^2 2 R
Therefore, Answer= 2 Pi R^3

Like? Yes (1) | No

Harsh Poddar 9 years AGO

Radius of cylinder is equal to radius of sphere and height of cylinder is the diameter of sphere so volume=pi R^2h=2piR^3

Like? Yes (1) | No (1)

vivek 9 years AGO

radius of cylinder will be r and hight will be 2r.
volume will be pi*r*r*h= pi*r*r*2r=2*pi*r*r*r.

Like? Yes (3) | No (3)

Akash Kumar 9 years AGO

As sphere touches all the dimensions of the cylinder so radius and height of the of the cylinder are following..
r=R; h=2R,
so volume of cylinder is=pi*r^2*h=pi*(R)^2*(2R)=2 pi R^3
that's why answer is option 6

Like? Yes (1) | No (1)

Ajeet Kumar 9 years AGO

as it touches the top and bottom of the cylinder, so
h= 2r
volume= pi(r*r)h
=2pir^2h

Like? Yes (1) | No (1)

TINKU MITTAL 9 years AGO

as the sphere touches the base and top as well as side walls, so the radius of cylinder= radius of sphere= R
and height of cylinder= dia of sphere= 2R
so volume of cylinder= pi*R^2 *(2R)
= 2 pi R^3

Like? Yes (1) | No (1)

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Time: 00:01:33

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If a sphere is placed inside a right circular cylinder so as to touch the top, base and the lateral

M4maths Previous Puzzles

02 Sep 2015 Volume