If r₁ and r₂ denote the radii of the circular bases of the frustum of a cone such that r₁>r₂, then write the ratio of the height of the cone of which the frustum is a part to the height fo the frustum.
Answers
Answer:
The ratio of the height of a cone of the frustum is a part to the height of the frustum is h : h1 = r1 : (r1 - r2)
Step-by-step explanation:
SOLUTION :
Let r1 & r2 be the radius of the lower part of the frustum.
Radius of bottom of the frustum, OA = r1
Radius of top of the frustum, O’B = r2
Height of a cone , OV = h
Height of a Frustum, O’O = h1
Height of a smaller cone = O'V = h - h1
In ∆VO’B & ∆VOA,
∠∆VO’B = ∠VOA (each 90°)
∠VBO’ = ∠VAO (corresponding angles)
∆VO’B ~ ∆VOA [By AA Similarity]
O’B/OA = O'V/OV
[Corresponding sides of a similar triangles are proportional]
r2/r1 = (h - h1) /h
r2/r1 = h/h - h1 /h
r2/r1 = 1 - h1 /h
h1 /h = 1 - r2/r1
h1 /h = (r1 - r2)/r1
Ratio of the height of a cone of the frustum is a part to the height of the frustum, h: h1 = r1 : (r1 - r2)
Hence, the ratio of the height of a cone of the frustum is a part to the height of the frustum is h: h1 = r1 : (r1 - r2)
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