Question

quinn calculated the approximate volume of the cone shown using 3.14 for π. there is an error in quinns work. what error did quinn make, and what is the correct approximate volume? use the drop - down menus to explain. 10 cm 15 cm v = 1/3(3.14)(10²)(15) cm³ v = 2,355 cm³ click the arrows to choose an answer from each menu. in the calculation for volume, quinn choose... the correct approximate volume of the cone is choose... cubic centimeters.

Explanation:

Step1: Recall volume formula

The volume formula for a cone is $V = \frac{1}{3}\pi r^{2}h$, where $r$ is the radius and $h$ is the height. Here, $r = 10$ cm and $h=15$ cm and $\pi = 3.14$.

Step2: Identify the error

Quinn used $\frac{1}{2}$ instead of $\frac{1}{3}$ in the volume - formula calculation.

Step3: Calculate the correct volume

Substitute the values into the correct formula:
\[

$$\begin{align*} V&=\frac{1}{3}(3.14)(10^{2})(15)\\ &=\frac{1}{3}(3.14)(100)(15)\\ &=(3.14)(100)(5)\\ & = 1570\text{ cm}^3 \end{align*}$$

\]

Answer:

In the calculation for volume, Quinn used the wrong formula coefficient (used $\frac{1}{2}$ instead of $\frac{1}{3}$). The correct approximate volume of the cone is $1570$ cubic centimeters.