Question

The height of a cone is 120cm. A small cone is cut off parllel to its base and its volume is 1/54 th the volume of original cone the heights of original conw is​

Answer 1

Answer:

The height from the base at which the section is made  will be 90 cm

Step-by-step explanation:

Since the smaller cone and larger cones are similar to each other

hence their radius and heights are proportional to each other

=> R/r = H/h = constant = k

where R = radius of larger cone

r = radius of smaller cone

H = height of big cone

h = height of small cone

Given their volume are in the ratio of 64 : 1

=> V/v = 64

=> (πR²H/3)/(πr²h/3) = 64

=> R²/r² x H/h = 64

=> k² x k = 64

=> k³ = 64

=> k = 4

Hence H/h = k = 4

=> 120/h = 4

=> h = 30 cm

Hence the height from the base at which the section is made = 120 - 30

= 90 cm