Advertisement Remove all ads

A Hollow Sphere of Internal and External Diameter 4cm and 8cm is Melted into a Cone of Base Diameter 8cm. Calculate Height of Cone? - Mathematics

A hollow sphere of internal and external diameter 4cm and 8cm is melted into a cone of base diameter 8cm. Calculate height of cone?

Advertisement Remove all ads

Solution

Given internal diameter of hollow sphere (r) = 4cm 

External diameter (R) = 8cm

Volumeof hollow sphere = `4/3pi(R^2-r^2)`

`=4/3pi(B^2 - 4^2)`         ____(1)

Given diameter of cone = 8cm 

Radius of cone = 4cm

Let height of cone be h

Volume of cone `=1/3pir^2h`

`=1/3xxpi(4)^2h`          ____(2)

Since hollow sphere is melted into a cone so there volumes are equal

(1) = (2)

⇒ `4/3pi(64-16)=1/3pi(4)^2h`

⇒`(4/3pi(48))/(1/3pi(16))=h`

⇒ h = 12cm

∴Height of cone = 12cm

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Exercise 14.1 | Q 25 | Page 29
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×