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  1. 8.1 cm
  2. 19.764 cm
  3. 9.6 cm
  4. 6.8 cm
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1 Answers

Option 1 : 8.1 cm

Given :

A cone was cut parallel to its base into 2 pieces

The ratio of the volume of the smaller cone formed and another part is 64: 61

The height of the cone = H = 40.5 cm

The height from the base at which the cut was made is to be calculated

Formula Used:

The volume of cone = πr2h/3

Concept Used:

If r and R are the radii of smaller cone and whole cone 

And h and H are the radii of smaller cone and whole cone 

Then r/R = h/H

Calculation:

Let the height  from base at which cut was made be 'h'

Since, Cone was cut parallel to its base into 2 pieces

Height of upper cone = H – h =  (40.5 – h) cm

The volume of upper cone =   1/3 × π × r² × (40.5 - h)

The volume of whole cone =   1/3 × π × R² × 40.5

Now, Ratio of volume = 1/3 × π × r² × (40.5 - h) : 1/3 × π × R² × 40.5

⇒  r² × (40.5 - h) : R² × 40.5 = 64 : (64 + 61)

⇒  r² × (40.5 - h) : R² × 40.5 = 64 : 125

Now, according to the concept used, r/R = (40.5 - h)/40.5

⇒ (40.5 - h)3 : 40.53 = 64 : 125

⇒ (40.5 - h) : 40.5 = 4 : 5

⇒ (40.5 - h) = 32.5

⇒ h = 8.1

∴ Height from the base where cut is made =  8.1 cm

 

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