# Carpentry & Building Construction

## Math Activities :

### Volume of a Rectangular Prism

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A prism is a three-dimensional figure whose ends, or bases, are parallel polygons. Its sides, or faces, are parallelograms. A parallelogram is a four-sided flat figure whose opposite sides are parallel and equal.

A polygon has three or more sides, so the bases of a prism have three or more sides. The bases can be triangles, squares, rectangles, etc. A rectangular prism has rectangular bases. The four faces of the rectangular prism are at right angles to the bases. Carpenters sometimes have to figure the volume of a space that is a rectangular prism. For example, excavations or concrete forms may be in this shape.

To find the volume of a rectangular prism, multiply length × width × height. The formula is V=lwh. Volume is measured in cubic inches, cubic feet, or cubic yards.

 Terms, Symbols, & Abbreviationsprism-three-dimensional figure whose bases are parallel polygonsparallelogram-four-sided flat figure whose opposite sides are parallel and equalrectangular prism-an object with rectangular bases and four sides that are at right angles to the basesvolume-the space inside a three-dimensional figurecu. in.-cubic inch, or cubic inches. The amount of space inside an object that is one inch long, one inch wide, and one inch high.cu. ft.-cubic foot, or cubic feet. One cubic foot contains 1,728 cubic inches.cu. yd.-cubic yard, or cubic yards. One cubic yard contains 27 cubic feet.

Practice Exercise

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Given length = 10 feet, width = 5 feet, and height = 4 feet, find the volume of the rectangular prism.

 Step 1 Use the formula V = lwh Step 2 Insert the given values. V = 10 × 5 × 4 Step 3 V = 200

The volume of the rectangular prism is 200 cubic feet

Problem Exercises

 1 Find the volume of an excavation whose length is 20', width is 14', and depth (height) is 8'. A) 2420 cu. ft. B) 35 cu. ft. C) 42 cu. ft. D) 2240 cu. ft. 2 Find the volume of a concrete form whose length is 13', width is 8', and depth (height) is 15'. A) 36 cu. ft. B) 1560 cu. yd. C) 780 cu. ft. D) 1560 cu. ft. 3 Find the volume of an excavation whose length is 100', width is 50', and depth (height) is 10'. A) 500 cu. ft. B) 2500 cu. ft. C) 5000 cu. ft. D) 50,000 cu. ft. 4 Find the volume of a sediment pond whose approximate length is 30', width is 8', and depth (height) is 5'. A) 1000 cu. ft. B) 1200 cu. ft. C) 400 cu. ft. D) 800 cu. ft. 5 Find the volume of an excavation whose length is 75', width is 30', and depth is 16'. A) 12,000 cu. ft. B) 1680 cu. ft. C) 36,000 cu. ft. D) 3,000 cu. ft.