# 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?

#### 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

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

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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 14 Surface Areas and Volumes
Exercise 14.1 | Q 25 | Page 29