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Home » A hollow sphere of internal and external diameters and respectively is melted into a cone of base diameter 8 cm. Calculate the height of the cone?
A hollow sphere of internal and external diameters 4cm and 8cm respectively is melted into a cone of base diameter 8 cm. Calculate the height of the cone?
CBSE | Class 10 | Exercise 16.1 | Maths | RD Sharma | Surface Areas And Volumes
A hollow sphere of internal and external diameters 4cm and 8cm respectively is melted into a cone of base diameter 8 cm. Calculate the height of the cone?

According to the question it is given that,

Internal diameter of hollow sphere =4cm

So, the internal radius of hollow sphere =2cm

External diameter of hollow sphere =8cm

So, the external radius of hollow sphere =4cm

As we know that,

Volume of the hollow sphere 4/3\pi \times \left( {{4}^{3}}-{{2}^{3}} \right)          … (i)

It is given that,

Diameter of the cone =8cm

Now, the radius of the cone =4cm

Assume the height of the cone be x cm

Volume of the cone 1/3\pi \times {{4}^{2}}\times h        ….. (ii)

As the volume of the hollow sphere and cone are equal. We can equate equations (i) and (ii)

Then, we get

4/3\pi \times \left( {{4}^{3}}-{{2}^{3}} \right)=1/3\pi \times {{4}^{2}}\times h

4\times \left( 64-8 \right)=16\times h

h=14

Therefore, the height of the cone so obtained will have a height of 14cm

i

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