Question

a disposable cup is in the shape of a cone, as shown. the cup has a volume of about 48.8 in³. what is the radius of the cup to the nearest inch?
? in.
6 in.
in.

Explanation:

Step1: Recall Cone Volume Formula

The volume \( V \) of a cone is given by \( V = \frac{1}{3}\pi r^2 h \), where \( r \) is the radius and \( h \) is the height. We know \( V = 48.8 \, \text{in}^3 \) and \( h = 6 \, \text{in} \).

Step2: Substitute Values into Formula

Substitute \( V = 48.8 \) and \( h = 6 \) into the formula:
\( 48.8 = \frac{1}{3}\pi r^2 (6) \). Simplify the right - hand side: \( \frac{1}{3}\times6 = 2 \), so the equation becomes \( 48.8 = 2\pi r^2 \).

Step3: Solve for \( r^2 \)

Divide both sides by \( 2\pi \): \( r^2=\frac{48.8}{2\pi}\approx\frac{48.8}{6.28}\approx7.77 \).

Step4: Solve for \( r \)

Take the square root of \( r^2 \): \( r=\sqrt{7.77}\approx2.79 \approx 3 \) (to the nearest inch).

Answer:

3