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horsena [70]
1 year ago
6

A​ cone-shaped paper water cup has a height of 12 cm and a radius of 6 cm. If the cup is filled with water to one-sixth its​ hei

ght, what portion of the volume of the cup is filled with​ water?
Mathematics
1 answer:
Liono4ka [1.6K]1 year ago
8 0

Answer:

  1/216

Step-by-step explanation:

The ratio of volumes of similar shapes is the cube of the scale factor. The filled portion of the cone is similar to the entire cone.

<h3>Linear scale factor</h3>

If the filled height is 1/6 of the total height, the scale factor for linear dimensions is 1/6.

<h3>Volume scale factor</h3>

The scale factor for the volume is the cube of the scale factor for linear dimensions. it is ...

  (1/6)³ = 1/216

The volume of the filled portion of the cup is 1/216 of the volume of the cup.

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