12.4 Vol of prisms & Cylinders

12.4 Vol of prisms & Cylinders - 12.4 Volume of...

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Unformatted text preview: 12.4 Volume of Prisms & Cylinders Cylinders p. 743 Volume of a solid Volume • Defn – the amount of space inside the solid. solid. • Just think “how much water would it Just take to fill the object”? take • Measured in cubic units (i.e. cm3) Post. 27 – Volume of a cube Post. V = s3 V – volume & s – edge length Ex: find the volume of the cube. V = s3 V = 53 V = 125 m3 5m Post. 28 – Volume ≅ post. Post. • If 2 polyhedra are ≅ , then they If then have the same volume. have Post. 29 – Volume + post. Post. • The volume of a solid is the sum of the The volumes of its non-overlapping parts. volumes Total volume volume volume = of + of of tower pyramid prism of Thm 12.6 – Cavalieri’s Principle Thm • If 2 solids have the same height & the If same cross-sectional area at every level, then they have the same volume. level, • Basically, this means that right & Basically, oblique solids use the same volume formulas, unlike surface area & lateral area formulas. area Thm 12.7 – Volume of a Prism Thm V = Bh V – volume, B – area of the base, & volume, h – height of the prism. height Ex: find the volume of the prism. Ex V = Bh B = ½ bh = ½ (2.5)(6) = 7.5 V = (7.5)(3) m m V = 22.5 mm3 2.5 mm 3 6 mm Thm 12.8 – Volume of a Cylinder Thm V = Bh Or V = π r2h Ex: Find the vol. of the cylinder. V = π r2h V = π (42)(13) V = π (16)(13) 13 ft V = 208π ft3 or 653.45 ft3 4 ft Ex: If the volume of the prism is 396 Ex If cm3, then what is the value of x? cm V = Bh 396 = (11x)(x) 396 = 11x2 36 = x2 6=x x = 6 cm 11 cm x cm x cm Hint: Find the volume of Find the whole block 1st, then the then subtract out the volume of the holes! the 13.5 in 4 in (whole block) V = Bh = (13.5*4)(3) = 162 in2 (1 hole) V = Bh = (3*6)(3) = 54 in3 (2 holes) V = 2(54) = 108 in3 Volume of concrete = 162 – 108 = 54 in3 * If concrete weighs 0.084 lbs/in3, how much how does this block weigh? does 0.084 * 54 = 4.536 lbs 3 in Ex: Find the Ex Find volume of the concrete block. concrete 3 in 6 in Assignment Assignment ...
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