A cone was cut parallel to its base into 2 pieces in such a way that the ratio of volume of smaller cone formed and other part is 64:61 .if the height of the cone is 40.5cm then find the height from the base at which the cut was made.
Answers
Given :
A cone was cut parallel to its base into 2 pieces in such a way that the ratio of volume of smaller cone formed and other part is 64 : 61
The height of the cone = H = 40.5 cm
To Find :
The height from the base at which the cut was made
Solution :
Total height of cone = H = 40.5 cm
Let , The height from the base at which the cut was made = h
∵ Cone was cut parallel to its base into 2 pieces
Height of upper cone = H - h = (40.5 - h) cm
Height of lower cone = h cm
∵ The volume of cone = × π × radius² × height
= × π × r² × h
Volume of upper cone = × π × r² × (40.5 - h)
Volume of lower cone = × π × r² × ( h)
∵ The ratio of volume of upper cone to volume of lower cone = 64 : 61
i.e =
Or, =
Or, 61 ( 40.5 - h ) = 64 h
Or, 2430 - 61 h = 64 h
Or, 64 h + 61 h = 2430
Or, 125 h = 2430
∴ h =
i.e h = 19.44 cm
Height = h = 19.44 cm