Question

leah likes getting her hair done at hair forever because they offer free drinks in the waiting room. the cups for hot drinks are cylindrical with a height of 9 centimeters and a radius of 3.8 centimeters. what is the volume of each hot - drink cup?
round your answer to the nearest whole number.
cubic centimeters
for cold drinks, there are cone - shaped paper cups. they have the same volume as the hot - drink cups and a radius of 5.1 centimeters. what is the height of each paper cup?
round your answer to the nearest whole number.
centimeters

Explanation:

Step1: Calculate the volume of the cylindrical cup

The formula for the volume of a cylinder is \(V = \pi r^{2}h\). Given \(r = 3.8\) cm and \(h=9\) cm.

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Rounding to the nearest whole number, \(V\approx408\) cubic centimeters.

Step2: Calculate the height of the conical cup

The formula for the volume of a cone is \(V=\frac{1}{3}\pi r^{2}h\). We know \(V = 408\) (from the cylinder's volume) and \(r = 5.1\) cm.

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Answer:

408 cubic centimeters
15 centimeters