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A cone is cut into two parts by a plane parallel to its base. Volume of the upper part which is a cone is 245 cm3. If the height of lower part is double of the height of upper part, then what is the volume of the lower part?

A cone is cut into two parts by a plane parallel to its base. Volume of the upper part which is a cone is 245 cm3. If the height of lower part is double of the height of upper part, then what is the volume of the lower part? Correct Answer 6370 cm<span style="position: relative; line-height: 0; vertical-align: baseline; top: -0.5em;font-size:10.5px;">3</span>

Given:

Volume of the upper part which is a cone = 245 cm3

Formula used:

Volume of the cone = 1/3π r2h

Where, r = radius, h = height

Calculation:

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According to the question,

ΔADE ∼ ΔABC

Then, AD : BC = 1 : 3

Let the radius of upper and lower be x, and 3x respectively

According to the question,

Volume of cone AFE : Volume of cone AGC

⇒ 1/3πxh : 1/3π(3x)33h

⇒ 1 : 27

Volume of cone AFE = 245

⇒ x = 245

Volume of cone AGC = 27x = 245 × 27 = 6615 cm3

Volume of the lower part = Volume of cone AGC - Volume of cone AFE = 6615 - 245 = 6370 cm3

∴ Volume of the lower part is 6370 cm3.

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