Question

A Church spire in a form of a regular hexagonal pyramid whose base edge is 8ft and whose altitude is 75ft is to be painted at a cost of 22 dollars per sq. yard. What is the total cost?

Answer 1

Answer:

The total cost is $4825.19.

Explanation:

Given information:

Base edge = 8 ft

Height = 75 ft

The surface area of a regular hexagonal pyramid is

$Area=\frac{3\sqrt{3}}{2}a^2+3a\sqrt{h^2+\frac{3a^2}{4}}$

where, a is base edge and h is height.

Substitute a=8 and h=75 in the above formula.

$Area=\frac{3\sqrt{3}}{2}(8)^2+3(8)\sqrt{(75)^2+\frac{3(8)^2}{4}}$

$Area=\frac{3\sqrt{3}}{2}(64)+3(8)\sqrt{5625+48}$

$Area\approx 166.28+1807.66$

$Area\approx 1973.94$

The area of regular hexagonal pyramid is 1973.94 sq. ft.

We know that

1 sq. yard = 9 sq. ft

The area of regular hexagonal pyramid in square yard is

$\frac{1973.94}{9}\approx 219.3267$

It is given that cost of paint is 22 dollars per sq. yard. So, total cost is

$\text{Total cost}=219.3267\times 22=4825.1874\approx 4825.19$

Therefore the total cost is $4825.19.

Answer 2

Given:
base edge - 8 ft
altitude or height - 75 ft

Surface area = [(3√3)/2] a² + 3a[√h² + (3a²/4)]
S.A = 2.6*8² + 3(8) * √75² + [(3*8²)/4]
S.A = 166.4 + 24 * √5625 + 48
S.A = 166.4 + 24 * √5674
S.A = 166.4 + 24 * 75.33
S.A = 166.4 + 1807.92
S.A = 1974.32 ft²

convert square feet to square yard.

1 sq ft = 0.1111 sq yd

1974.32 ft² * 0.1111 sq.yd/sq.ft = 219.35 sq yd.

22 per sq. yard

219.35 sq. yard * $22/sq.yd = $4,825.70

Total cost is $4,825.70