Kindly show solution and figure.

12. A trough (a solid figure that looks like a triangular prism) has triangular ends, which lie in parallel planes. The top of the trough is a horizontal rectangle 15 in by 30 in. and the depth of the trough is 12 in.

a. How many gallons of water will it hold?

b. Find the wetted surface when the depth of the water is 6 in. (one gal.

= 231 cubic inches)

13. A block of lead has the shape of rectangular solid whose dimensions are cm x cm x 1 cm. This piece of lead is to be melted and recast into the form of regular triangular prism each basal edges of which is to be cm. What must

be the altitude of this prism?

14. A manufacturer has been using, for shipping goods, wooden boxes 3 x 5 x 6 ft. He replaces these boxes with cubical boxes made up of boards of the same thickness and each requiring the same amount of lumber as formerly. What is the length of an edge of the cubical box?