A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. The radius o

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07 Apr 2016 Radius of the base

A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. The radius of the base of the cone is

OPtion

1) Sqrt10 cm
2) sqrt15 cm
3) 2 Sqrt3 cm
4) 2 Sqrt7 cm
5) Sqrt13 cm
6) Sqrt7 cm
7) 2 Sqrt6 cm
8) Sqrt14 cm
9) Sqrt17 cm
10)2 Sqrt2 cm

Solution

Volume of Hemi-sphere = Volume of cone
Therefore
2/3*Pi*7*7*7 = 1/3 Pi R^2*49
Solve
R = Sqrt14
Option 8)

Correct Option: 8 Best Solution (12)

ABHINAV PUSHPAM   8 years AGO

Let r be the radius of the base of the cone , then
pi*r^2*49 = 2/3*pi* 7^3
r = sqrt(14)
Option 8)

Like? Yes (6) | No (2)  

madanpal vishwakarma    8 years AGO

Volume of hemisphere = 2/3 pi r^3


volume of cone 1/3 pi r^2 because of of casting both voulme should be same

(2/3)pi (7^3) =(1/3)pi(r^2)49

after solving r= sqrt 14 cm

Like? Yes (3) | No (1)  

Saba umrani   8 years AGO

Volume of hemisphere = 2/3 * 3.14*7*7*7=718.01
Volume of right circular cone = 3.14*r*r*(49/3)=718.01
Hence r = sqrt14cm where r is the base of right circular cone

Like? Yes (2) | No   

MRITUNJAY   8 years AGO

volume of hemisphere=volume of cone
2/3?*r^3=1/3?*r^2*h
2/3*?*7*7*7=1/3*?*49*r^2
r^2=14
so r =?14
option 8

Like? Yes (1) | No   

RAHUL KUMAR   8 years AGO

Let the radius of the cone be R cm.
then,
1/3*π* R^2*49 = 2/3*π*7*7*7
R^2 = (2*7*7*7)/49 = 14
R = √14 cm.
option (8).

Like? Yes (1) | No   

Mukund Manohar   8 years AGO

Volume of hemisphere = 2/3 * 22/7 * 7*7*7
Volume of Cone = 1/3 * 22/7 * r*r * 49
Both volumes are equal
2 * 7*7*7 = r*r * 49
r = Sqrt14 cm

Like? Yes (1) | No   

Dinesh kumar sah   8 years AGO

simply volume of hemisphere and volume of cone are equal.
2/3?r^3=1/3?r^2h-------(1)
if we put the radius of hemisphere i.e 7cm and height of cone i.e 49 cm then we will get the radius of the base of the cone is sqrt 14cm. i.e option (8) is the correct answer.

Like? Yes (2) | No (1)  

ANANTHA PADMANABHAN T   8 years AGO

if the radius of cone is sqrt14 then the volume of cone and hemisphere becomes equal therefore the hemisphere can be cast into the cone

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Asheesh Jain   8 years AGO

Volume of hemisphere = 2/3TTr3
= 2/3TT(7)3
= 686/3TT cm3
Volume of cone = 1/3TTr2h
= 1/3TTr2(49)
= 49/3TTr2 cm3
Now,
Volume of cone = Volume of hemisphere
49/3TTr2 = 686/3TT
r2 = 14
r = √14 cm

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SUDHIR   8 years AGO

Volume of hemisphere= Volume of cone
After calculating the value r=sqrt 14.

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VIJAY KIRAN   8 years AGO

volume of hemisphere is (2/3)*pi*(R^3)
volume of cone=pi*(r^2)*h
substitute R=7 and h=49,and equating those two volume we get r=sqrt(14)

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shailesh kumar shashi   8 years AGO

vol. of hsphere = vol of cone
on caln_
(r)2= 14
hence, r=?14

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