Question

a glass holds about 500 milliliters of water and has a diameter of 6 centimeters.
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 \( d = 6 \) cm, so the radius \( r=\frac{d}{2}=\frac{6}{2} = 3 \) 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 \( V = 500 \) \( \text{cm}^3 \) (since \( 1 \) mL \( = 1 \) \( \text{cm}^3 \)), \( \pi\approx3.14 \), and \( r = 3 \) cm. Substitute these values into the formula: \( 500=3.14\times3^{2}\times h \).

Step3: Calculate \( 3^{2}\times3.14 \)

First, \( 3^{2}=9 \), then \( 9\times3.14 = 28.26 \). So the equation becomes \( 500 = 28.26h \).

Step4: Solve for \( h \)

Divide both sides of the equation by \( 28.26 \): \( h=\frac{500}{28.26}\approx17.7 \). Rounding to the nearest centimeter, \( h\approx18 \).

Answer:

\( 18 \)