the height of a cone is 120 CM a small cone is off at the top by a plane parallel to the base and its volume is1/64 the volume of the height from the bare of which the section is made is
Answers
hope it works ✌️
☺️☺️☺️☺️☺️
Answer ⇒ Height of the remaining part from the base = 90 cm.
Step-by-step explanation ⇒ Height of the Cone = 120 cm.
Volume of the Cutted Cone = 1/64 of V original.
Let the radius of the small cone cutted be x cm.
Therefore, Volume of the Cutted cone = 1/3 πx²h, where h is the Height of small cone.
Volume of the Original cone = 1/3 πR²H, H is the height of the Original cone = 120 cm.
∴ 1/3 πx²h = 1/64 × 1/3πR²(120)
x²h = R² × 120/64
(x/R)²h = 120/64 ----eq(i)
Now, Refer to the attachment,
From the figure,
h/120 = x/R
x/R = h/120
Putting this in the eq(i),
(h/120)² × h = 120/64
∴ h³ = (120 × 120 × 120)/64
∴ h³ = (120/4)³
On Comparing,
h = 120/4
∴ h = 30 cm.
Therefore, Height of the remaining part from the base = H - h
= 120 - 30
= 90 cm.
Hope it helps.
