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Home » 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
CBSE | Class 10 | Exercise 12.1 | Maths | NCERT Exemplar | Surface Areas And Volumes
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

(B) 14cm

NCERT Exemplar Class 10 Maths Chapter 12 Ex. 12.1 Question 9

Volume of circular shell = Volume of cone recast by liquefying

For Spherical Shell,

Inside measurement, d1 = 4 cm

Inside range, r1 = 2 cm

[ as range = 1/2 diameter]

Outer measurement, d2 = 8 cm

Outer range, r2 = 4 cm

Presently,

As volume of circular shell

    \[=\text{ }4/3\text{ }\pi \text{ }\left( r23\text{ }\text{ }r13 \right)\]

where r1 and r2 are inside and outside radii individually.

volume of given shell

    \[=\text{ }4/3\text{ }\pi \text{ }\left( 43\text{ }\text{ }23 \right)\]

    \[=\text{ }4/3\text{ }\pi \text{ }\left( 56 \right)\]

    \[=\text{ }\left( 224/3 \right)\text{ }\pi \]

We realize that,

Volume of cone = 224π/3 cm3

For cone,

Base width = 8 cm

Base range, r = 4 cm

Let Height of cone = ‘h’.

We know,

Volume of cone

    \[=\text{ }\left( 1/3 \right)\text{ }\pi \text{ }r2h,\]

Where r = Base range and h = tallness of cone

Volume of given cone

    \[=\text{ }\left( 1/3 \right)\text{ }\pi \text{ }42h\]

    \[\Rightarrow 224\pi /3\text{ }=\text{ }16\pi h/3\]

    \[\Rightarrow 16h\text{ }=\text{ }224\]

h = 14 cm

Along these lines, Height of cone is 14 cm.

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