Answer to Question #168256 in Geometry for AYRIAH

Question

A pottery manufacturer has made 50 hanging vases each to hold 1 pint of water when full. The vases are in the form of pentagonal pyramid. The area of the pentagon when cut out of the plane of the base by the lateral faces is 9 sq. in. The height of the base is 1 ft. (Fig. 4.2.4). Compute the total weight of the 50 vases if each weighs 150 lbs. per cu. ft.

Answer 1

$1ft=12in$

$$V_{out}=\dfrac{1}{3}Sh=\dfrac{1}{3}9(12)=36(in^3)$$

$$V_{in}=1\ pint=28.875\ in^3$$

$$V=36-28.875=7.125(in^3)$$

$$1\ lbs/ ft^3=453.59237\ g/(1728 in^3)$$

$$m_{vase}=7.125(150)(\dfrac{453.59237}{1728})=280.542(g)$$

$$M=280.542(50)=14027(g)=14\ kg\ 27\ g$$

The total weight of the 50 vases is 14 kg 27 g.