Question

1. the triangle is rotated around the indicated ax what is the volume of the resulting figure? a) 75π cm³ b) 225π cm³ c) 405π cm³ d) 135π cm³

Explanation:

Step1: Identify the resulting solid

When a right - angled triangle is rotated around one of its legs, the resulting solid is a cone. Here, if we rotate the given right - angled triangle around the vertical leg of length 9 cm, the radius of the base of the cone $r = 5$ cm and the height of the cone $h=9$ cm.

Step2: Recall the volume formula for a cone

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$.

Step3: Substitute the values of $r$ and $h$ into the formula

Substitute $r = 5$ cm and $h = 9$ cm into the formula $V=\frac{1}{3}\pi r^{2}h$. We get $V=\frac{1}{3}\pi\times5^{2}\times9$.
First, calculate $5^{2}=25$, then $25\times9 = 225$, and $\frac{1}{3}\times225 = 75$. So $V = 75\pi$ $cm^{3}$.

Answer:

a) $75\pi$ $cm^{3}$