Question

a glass holds about 500 milliliters of water and has a diameter of 7 centimeters.
d = 7 cm
h = ? cm
how tall is the glass to the nearest centimeter?
use 3.14 to approximate π. 1 ml = 1 cm³
h ≈ □ cm

Explanation:

Step1: Find the radius of the glass

The diameter \( d = 7\) cm, so the radius \( r=\frac{d}{2}=\frac{7}{2} = 3.5\) cm.

Step2: Recall the volume formula for a cylinder

The volume \( V\) of a cylinder is given by \( V=\pi r^{2}h\). We know that \( V = 500\) \(cm^{3}\) (since \( 1\) mL \( = 1\) \(cm^{3}\)) and \( \pi\approx3.14\), \( r = 3.5\) cm. We need to solve for \( h\). Rearranging the formula for \( h\), we get \( h=\frac{V}{\pi r^{2}}\).

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

\( r^{2}=(3.5)^{2}=12.25\).

Step4: Calculate \( \pi r^{2}\)

Substitute \( \pi = 3.14\) and \( r^{2}=12.25\) into \( \pi r^{2}\): \( 3.14\times12.25 = 38.465\).

Step5: Calculate \( h\)

Now, substitute \( V = 500\) and \( \pi r^{2}=38.465\) into the formula for \( h\): \( h=\frac{500}{38.465}\approx13\) (rounded to the nearest centimeter).

Answer:

\(13\)