Volume The space a figure occupies measured in cubic units (in 3, ft 3, cm 3 )
Cavalieri’s Principle If two space figures have the same height & the same cross-sectional area at every level, then they have the same volume.
Volume of a Prism You can find the volume of a right prism by multiplying the area of the base by the height. By Cavalieri’s Principle, you can extend this idea to any prism. V = Bh
Find the volume of the prism below. The area of the base B = w = 3 5 = 15. V = BhUse the formula for volume. = 15 5Substitute 15 for B and 5 for h. = 75Simplify. The volume of the rectangular prism is 75 in. 3.
Find the volume of the prism below. The prism is a right triangular prism with triangular bases. The base of the triangular prism is a right triangle where one leg is the base and the other leg is the altitude. 29 2 – 20 2 = 841 400 = 441 21 Use the Pythagorean Theorem to calculate the length of the other leg.
The volume of the triangular prism is 8400 m 3. The area B of the base is bh = (20)(21) = 210. Use the area of the base to find the volume of the prism. 1212 1212 V = BhUse the formula for the volume of a prism. = 210 40Substitute. = 8400Simplify. (continued)
Find the volume of the cylinder below. Leave your answer in terms of. The volume of the cylinder is 576 ft 3. V = r 2 hUse the formula for the volume of a cylinder. The formula for the volume of a cylinder is V = r 2 h. The diagram shows h and d, but you must find r. r = d = 8 1212 = 8 2 9Substitute. = 576Simplify.
Find the volume of the composite space figure. You can use three rectangular prisms to find the volume. Each prism’s volume can be found using the formula V = Bh.
Volume of prism I = Bh = (14 4) 25 = 1400 Volume of prism II = Bh = (6 4) 25 = 600 Volume of prism III = Bh = (6 4) 25 = 600 Sum of the volumes = 1400 + 600 + 600 = 2600 The volume of the composite space figure is 2600 cm 3. (continued)