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  • A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form a cone of base diameter 8cm. The height of the cone is (A) 12cm (B) 14cm (C) 15cm (D) 18cm

A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively is melted and recast into the form a cone of base diameter 8cm. The height of the cone is

(A) 12cm
(B) 14cm
(C) 15cm
(D) 18cm

Answers (1)

best_answer

Answer(B) 14cm

Solution
The external diameter of a metallic shell = 8cm
Radius

=R_{1}=\frac{8}{2}=4cm
The internal diameter of a metallic shell = 4 cm
Radius

=R_{2}=\frac{4}{2}=2cm

The volume of spherical shell

=\frac{4}{3}\pi (4^{3}-2^{3})
      =\frac{4}{3}\pi (64-8)=\frac{4}{3} \pi (56)=\frac{224}{3}\pi
It is given that volume of a cone = volume of the shell
Volume of cone 

 =\frac{224}{3}\pi
The formula of value of cone is

=\frac{1}{3}\pi r ^{2} h
Diameter of cone = 8 cm
Radius = 4 cm
\Rightarrow \frac{1}{3}\pi r^{2}h=\frac{224}{3}\pi
\Rightarrow \frac{1}{3}\pi (4^{2})h=\frac{224}{3}\pi
h=\frac{224}{4\times 4}=14cm

Posted by

infoexpert26

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