Question

quinn calculated the approximate volume of the cone shown using 3.14 for π. there is an error in quinn’s work. what error did quinn make, and what is the correct approximate volume? use the drop-down menus to explain.
diagram of a cone with a horizontal segment labeled 10 cm and a vertical segment labeled 15 cm. next to the cone: ( v = \frac{1}{2}(3.14)(10^2)(15) , \text{cm}^3 ), ( v = 2,355 , \text{cm}^3 )
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 Cone 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. Quinn used \( \frac{1}{2} \) instead of \( \frac{1}{3} \) in the formula.

Step2: Identify Radius and Height

From the diagram, the radius \( r = 10\space cm \) and height \( h = 15\space cm \), \( \pi = 3.14 \).

Step3: Calculate Correct Volume

Substitute values into the correct formula:
\( V=\frac{1}{3}(3.14)(10^{2})(15) \)
First, calculate \( 10^{2}=100 \).
Then, \( \frac{1}{3}(3.14)(100)(15)=\frac{1}{3}(3.14)(1500) \).
\( 3.14\times1500 = 4710 \), then \( \frac{4710}{3}=1570 \).

Answer:

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