Question

a paper cup holds about 200 milliliters of water and has a diameter of 9 centimeters.
what is the height of the paper cup to the nearest centimeter?
use 3.14 to approximate π. 1 ml = 1 cm³
h ≈ □ cm

Explanation:

Step1: Recall the volume formula for a cone

The volume \( V \) of a cone is given by the formula \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height. We know that the volume of water the cup holds is \( 200 \) milliliters, and since \( 1\space mL = 1\space cm^{3} \), the volume \( V = 200\space cm^{3} \). The diameter \( d = 9\space cm \), so the radius \( r=\frac{d}{2}=\frac{9}{2}= 4.5\space cm \), and \( \pi\approx3.14 \).

Step2: Substitute the known values into the formula

Substitute \( V = 200 \), \( r = 4.5 \), and \( \pi=3.14 \) into the volume formula:

$$ 200=\frac{1}{3}\times3.14\times(4.5)^{2}\times h $$

Step3: Calculate \( (4.5)^{2} \)

First, calculate \( (4.5)^{2}=4.5\times4.5 = 20.25 \)

Step4: Simplify the right - hand side of the equation

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So our equation becomes \( 200 = 21.195h \)

Step5: Solve for \( h \)

To find \( h \), we divide both sides of the equation by \( 21.195 \):
\( h=\frac{200}{21.195}\approx9.436 \)

Step6: Round to the nearest centimeter

Rounding \( 9.436 \) to the nearest centimeter gives \( h\approx9 \)

Answer:

\( 9 \)