Question

select the correct answer.
a conical paper cup has dimensions as shown in the diagram. how much water can the cup hold when full?
a. 30π cm³
b. 35π cm³
c. 40π cm³
d. 45π cm³

Explanation:

Step1: Find radius of the cone

The diameter is 6 cm, so radius $r = \frac{6}{2} = 3$ cm.

Step2: Recall cone volume formula

Volume formula: $V = \frac{1}{3}\pi r^2 h$

Step3: Substitute values and calculate

Substitute $r=3$ cm, $h=10$ cm:

$$\begin{align*} V&=\frac{1}{3}\pi (3)^2 (10)\\ &=\frac{1}{3}\pi (9)(10)\\ &=30\pi \end{align*}$$

Answer:

A. $30\pi \text{ cm}^3$