A cone is divided into two parts by drawing a plane through mid points of it axis and parallel to its base compare to volumes
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Let r be radius of smaller cone
Let R be radius of bigger cone
See figure, We got right angled triangle:
So, x/2x = r/R ⇒ 1/2 = r/R ⇒ R/r = 2/1
Then comparing = volume of cone/ volume of frustum
= 1/3πr²x ÷ 1/3πx(r²+R²+Rr)
= 1 ÷ r²/r² + R²/r² + Rr/r
= 1 ÷ 1 + (R/r)² + R/r
= 1 ÷ 1+2²+2
= 1/7 or 1:7
Let R be radius of bigger cone
See figure, We got right angled triangle:
So, x/2x = r/R ⇒ 1/2 = r/R ⇒ R/r = 2/1
Then comparing = volume of cone/ volume of frustum
= 1/3πr²x ÷ 1/3πx(r²+R²+Rr)
= 1 ÷ r²/r² + R²/r² + Rr/r
= 1 ÷ 1 + (R/r)² + R/r
= 1 ÷ 1+2²+2
= 1/7 or 1:7
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