Question

question 8 (multiple choice worth 1 points) (06.03 mc)
the radius of the cone is 7 in and y = 25 in. what is the volume of the cone in terms of π?
image of a cone with height x, slant height y, and radius 7
392π in³
408π in³
112π in³
117π in³

Explanation:

Step1: Find the height of the cone

The slant height \( y = 25 \) in, radius \( r = 7 \) in. Using the Pythagorean theorem in the right triangle (height \( x \), radius \( r \), slant height \( y \)): \( x=\sqrt{y^{2}-r^{2}} \).
\[
x=\sqrt{25^{2}-7^{2}}=\sqrt{625 - 49}=\sqrt{576}=24
\]

Step2: Calculate the volume of the cone

The formula for the volume of a cone is \( V=\frac{1}{3}\pi r^{2}h \), where \( r = 7 \) in and \( h=x = 24 \) in.
\[
V=\frac{1}{3}\pi\times7^{2}\times24=\frac{1}{3}\pi\times49\times24 = 49\times8\pi=392\pi
\]
Wait, there seems to be a typo in the options? Wait, maybe I misread. Wait, let's check again. Wait, maybe the options have a typo, but let's recalculate. Wait, \( r = 7 \), \( h = 24 \). \( V=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi\times49\times24=\frac{49\times24}{3}\pi=49\times8\pi = 392\pi \). So if one of the options is \( 392\pi \) (maybe the first option was a typo, like 392π), then that's the answer.

Answer:

Assuming the first option is \( 392\pi \) (maybe a typo in the original), the volume is \( 392\pi \) cubic inches. So the correct option (if it's the first one) is: A. \( 392\pi \) in³ (assuming the first option was miswritten as 392π, as per calculation).