Question

all prisms and pyramids are regular. leave answers in exact form. 1) a = πr²×h 16 in 7 in volume = 784π 2) 11 cm 8 cm volume = 3) 15 in 13.76 in 20 in volume = 2380 4) what is the volume of a cone with a slant height of 15 m and a radius of 12 m? 5) what is the volume of a regular hexagonal prism with a base - side length of 16 ft and a height of 9 ft?

Explanation:

Step1: Recall volume formula for prism

The volume formula for a prism is $V = Bh$, where $B$ is the base - area and $h$ is the height. For a regular hexagonal prism, the base - area formula for a regular hexagon with side length $s$ is $B=\frac{3\sqrt{3}}{2}s^{2}$.

Step2: Calculate base - area of the hexagonal prism

Given $s = 16$ ft, then $B=\frac{3\sqrt{3}}{2}\times16^{2}=\frac{3\sqrt{3}}{2}\times256 = 384\sqrt{3}$ square - feet.

Step3: Calculate volume of the hexagonal prism

Given $h = 9$ ft and $B = 384\sqrt{3}$ square - feet, then $V=Bh=384\sqrt{3}\times9 = 3456\sqrt{3}$ cubic - feet.

Answer:

$3456\sqrt{3}\text{ ft}^3$