University:
High School
Course:
High School Geometry
Academic year:

2022
Views:

453

Pages:

2
Author:

klovenierw7

In your own words, write the meaning of each vocabulary term. Volume: the inside part of 3-D object Density: matter of an object Cavalieri's Principle: two solids with the same height and cross-areas (bases) have the same Volume Similar Solids: two 3-D objects that have the same shape Same scale factor for all sides Core Concepts Volume of a Prism The volume of a prism is V = Bh, where B is the area of a base and h is the height. Volume of a Cylinder The volume of a cylinder is V = Bh = πr²h, where B is the area of a base, h is the height, and r is the radius of a base. Think of this as a Prism with a circular Base Similar Solids Two solids of the same type with equal ratios of corresponding linear measures, such as heights or radii, are called similar solids. The ratio of the corresponding linear measures of two similar solids is called the scale factor. If two similar solids have a scale factor of k, then the ratio of their volumes is equal1 to k³. Extra Practice In Exercises 1 and 2, find the volume of the prism. v = B * h triangle (1/2 * b * h) * h (1/2 * 3 * 1.5) * 5 11.25 cm³ Area of base = 10 in² V = B * h (10) * 4 40 in³ In Exercises 3 and 4, find the volume of the cylinder. V = B * h circle (πr²) * h (π * 2.5²) * 7 43.75π in³ V = B * h circle (πr²) * h (π * 2²) * 11 44π cm³ In Exercises 5 and 6, find the indicated measure. height of a cylinder with a base radius of 8 inches and a volume of 2010 cubic inches 1 V = B * h 2010 = (π * 8²) * h 2010 = (64π) * h 2010 / 64π = h 9.9969 in ≈ h area of the base of a pentagonal prism with a volume of 50 cubic centimeters and a height of 7.5 centimeters V = B * h 50 = B * 7.5 50 / 7.5 = B 6.6667 cm² ≈ B In Exercises 7 and 8, find the missing dimension of the prism or cylinder. Volume = 661.5 cm³ V = B * h 661.5 = (3.5 * h) * 18 661.5 = 63h 10.5 cm = h Volume = 75.36 in³ V = B * h 75.36 = (πr²) * 6 75.36 / 6π = r² 3.999 ≈ r² 1.9995 in ≈ r