Question

A regular pentagonal pyramid had a side length of 4 mm, an apothem that measures 3 mm, and a height of 4.1 mm. What is the volume of the pyramid?



A) 41 mm^3
B) 63 mm^3
C) 16.4 mm^3
D) 60 mm^3

Answer 1

The equation for solving the volume of a pyramid is equal to,
                              Volume = Bh/3

where B is the area of the base and h is height. 
To compute for the area of the base, we use the equation,
                                A = aP/2
where a is apothem and P is perimeter. Substituting the known values,
                                A = (3 mm)(5 x 4 mm) / 2 = 30 mm²
Substituting the computed value to the equation for volume.
                          V = (30 mm²)(4.1 mm) / 3 = 41 mm³
Thus, the answer is letter A.