Question

score: 13/36 answered: 6/16 question 7 calculate the volume. do not round. v = ft³ submit question cone image with slant height 25 ft and diameter 14 ft

Explanation:

Step1: Find the radius of the cone

The diameter of the base is 14 ft, so the radius \( r=\frac{14}{2} = 7 \) ft.

Step2: Find the height of the cone

Using the Pythagorean theorem, the slant height \( l = 25 \) ft, radius \( r = 7 \) ft. Let the height be \( h \), then \( h=\sqrt{l^{2}-r^{2}}=\sqrt{25^{2}-7^{2}}=\sqrt{625 - 49}=\sqrt{576}=24 \) ft.

Step3: Calculate the volume of the cone

The formula for the volume of a cone is \( V=\frac{1}{3}\pi r^{2}h \). Substituting \( r = 7 \), \( h = 24 \), we get \( V=\frac{1}{3}\pi\times7^{2}\times24=\frac{1}{3}\pi\times49\times24 = 49\times8\pi=392\pi \) \( ft^{3} \).

Answer:

\( 392\pi \)