Answer:
vol = 62 in³
Step-by-step explanation:
First determine r (see attached image) by using pythagorean theorem.
a² = b² + c²
a = 3 in
b = 3/2 = 1.5 in
c = r
3² = 1.5² + r²
r = [tex]\sqrt{3^{2}-1.5^{2} }[/tex]
r = 2.598 in
Get the area = n/2 * a * r
n = number of sides = 6
r = 2.598 in
Area = 6/2 * 3 * 2.598
Area = 23.38 in²
get the volume = 1/3 * Area * h
Area = 23.38 in²
h = 8 in (as given)
vol = 1/3 * 23.38 * 8
vol = 62 in³
