Home
Class 9
MATHS
A cone id 8.4 cm height and the radius...

A cone id 8.4 cm height and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is .

A

4.2 cm

B

2.1 cm

C

2.4 cm

D

1.6 cm

Text Solution

Verified by Experts

The correct Answer is:
B
Given ,height of a cone = 8.4 cm
Radius of the base of cone = 2.1 cm
Volume of a cone `=(1)/(3) pir^(2)h = (1)/(3)xx pi xx (2.1)^(2) xx 8.4`
=`(1)/(3) xx pi xx 2.1 xx 2.1 xx 8.4 = pi xx 4.41 xx 2.8 cm^(3)`
Since, cone is melted and recast into a sphere.
Let the radius of a sphere be R.
Then, volume of a sphere = Volume of a cone
`rArr " "(4)/(3)pir^(3) = pi xx 4.41 xx 2.8 rArr r^(3) =(4.41 xx 2.8 xx 3)/(4)`
`rArr " "r^(3) = 4.41xx0.7xx3`
`rArr " "r^(3)= 4.41 xx 2.1`
`therefore" "r=2.1`
Hence , the radius of the sphere is 2.1 cm.
Promotional Banner

Topper's Solved these Questions

  • VOLUME AND SURFACE AREA

    NCERT EXEMPLAR ENGLISH|Exercise VERY SHORT ANSWER TYPE QUESTIONS|10 Videos

  • VOLUME AND SURFACE AREA

    NCERT EXEMPLAR ENGLISH|Exercise SHORT ANSWER TYPW QUESTIONS|10 Videos

  • TRIANGLES

    NCERT EXEMPLAR ENGLISH|Exercise LONG ANSWER TYPE QUESTIONS|21 Videos

Similar Questions

Explore conceptually related problems

A right circular cone is 8 cm high and radius of its base is 2 cm .The cone is metted and recaset in to a sphere. Determine the diameter of the sphere.

A right circular cone is 3.6 cm high and radius of its base is 1.6 cm. It is melted and recast into a right circular cone with radius of its base as 1.2 cm. Find its height.

A right circular cone is 3.6 cm high and radius of its base is 1.6 cm. It is melted and recast into a right circular cone with radius of its base as 1.2 cm. Find its height.

A right circular cone is 3.6 cm high and radius of its base is 1.6 cm. It is melted and recast into a right circular cone with radius of its base as 1.2 cm. Find its height.

A right circular cone is 3.6 cm high and radius of its base is 1.6 cm. It is melted and recast into a right circular cone with radius of its base as 1.2 cm. Find its height.

Threee metallic cones of radius 2cm and height 9 cm are melted and recast in to a solid sphere. Find the radius of the sphere.

Threee metallic cones of radius 2cm and height 9cm are melted and recast in to a solid sphere. Fuind the radius of the sphere.

A solid metallic right circular cone of height 30cm and radius of the base 12 cm is melted and two solid spheres formed from it. If the volume of one of the sphere is 8 times that of the other find the radius of the smaller sphere.

The base diameter and height of a metallic cone are 24cm and 6cm respectively .It is melted and recast in to a sphere.Find the surface area of the sphere.

A solid metallic right circular cone of height 6.75 cm and radius of the base 12 cm is melted and two solid sphees formed form it. If the volume of one of the sphere is 8 times that of the other find the radius of the smaller sphere.