Question

multiply the area of the base by the height to find a formula for the volume v of the solid. the formula for the volume v of the solid is v = (type an exact answer, using π as needed.)

Explanation:

Step1: Find area of the base

The base is a sector of a circle. The area of a full - circle is $A_{circle}=\pi r^{2}$. The area of a sector with central angle $\theta$ (in radians) is $A = \frac{\theta}{2\pi}\times\pi r^{2}=\frac{\theta r^{2}}{2}$.

Step2: Multiply base area by height

The volume of a solid is given by $V=A\times h$. Substituting the area of the base $A=\frac{\theta r^{2}}{2}$ into the volume formula, we get $V=\frac{\theta r^{2}h}{2}$.

Answer:

$V = \frac{\theta r^{2}h}{2}$