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VIJAY SINGH

· started a discussion

· 1 Months ago

you asked height from ground (Question: 111058.0 )

sir you have asked height from ground which is 30-10=20

Question:
The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. It its volume be \(\cfrac{1}{27}\) of the volume of given cone then the height above the base where the section is made, is :
Options:
A) 2 cm
B) 6 cm
C) 20 cm
D) 10 cm
Solution:
Ans: (c)


= \(\cfrac{1}{3}\pi R^2H\) 

= \(\cfrac{1}{3}\pi R^2\times30\)

= 10 \(\pi R^2 cm^2\)

Volume of small cone OCD 

= \(\cfrac{1}{3}\pi r^2h\)

\(\cfrac{1}{27}\)of volume of cone AOB 

h = \(\cfrac{10}{9}\left ( \cfrac {R}{r} \right )^2\)  

as \(\cfrac{R}{r}=\cfrac{30}{h}\)

\(\therefore h=\cfrac{10}{9}\left ( \cfrac {30}{h} \right )^2\)

h3 = 10 \(\times\) 100

h=\(\sqrt[3]{1000}\)

= 10 cm

so, H - h = 30 -10 = 20cm

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