Solid Mensuration Problems and Answers

Name: _______________________________________________ Date: __________________ ) 1. A trough is formed by nailing together, edge to edge, two boards 11 ft. In length, so that the right section is a right triangle. If 15 gal. Of water are poured into the trough and if the trough is held level so that a right section of the water is an isosceles right triangle, how deep is the watr? (231 cu.in. = 1 gal.)

2. Find the volume of water in a swimming pool with vertical ends and sides. The length measured at the water line is 50 ft. and the breadth is 20 ft. The bottom of the swimming pool is a plane sloping gradually downward so that the depth of the water at one end is 4ft. and at the other end is 8 ft.

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b 45o b 45o

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3. A model triangular block, as volume and house.

house is made by sticking a prism on top of a rectangular shown in the diagram. Find the total surface area of the model

4. The dimensions of a rectangular solid are in the ratio 1:3:12 and its volume is 562.5cm2. Find the volume of a cube whose surface area is equal to the surface area of the rectangular solid.

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Name: _______________________________________________ Date: __________________ 5. Two edges of the base of an oblique parallelepiped are 6cm and 10cm and with included angle of 45o. A lateral edge 12cm forms an angle of 60o with the base. Find the volume of the parallelepiped.

6. Find the area of the shaded portion, which is the area of the triangle ABC if the prism’s base is a regular polygon with BC=4ft and AD=8ft.

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Bonus: Write your solutions and answers at the back. Answer only this question if you are sure of your answer in number 6. If a vertical plane passed through the line connecting A and E in order to cut the prism into two different solid figures, what will be the volume of each of the figures formed?

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