University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

358

Pages:

3
Author:

Omari Mccormick

Volumes of Pyramids In your own words, write the meaning of each vocabulary term. pyramid 3-D Shapes that go to a point Bases can be any polygon shape composite solid a 3-D shape made up of two or more solids. trick is to separate the shapes and find them individually and +/- as necessary. Core Concepts Volume of a Pyramid The volume of a pyramid is V = 1/3 Bh where B is the area of a base and h is the height. 11.6 Extra Practice In Exercises 1-6, find the volume of the pyramid. 1. 9 cm 4 cm 6 cm most of the points here V = 1/3 Bh triangle (1/2 * 6 * 4) * 9 = 36 cm^3 2. 8 in 6 in V = 1/3 Bh square (6^2) * 8 = 96 in^3 3. 9 yd 4 yd 4 yd V = 1/3 Bh square (4^2) * 9 = 48 yd^3 4. 15 m 7 m 11 m V = 1/3 Bh rectangle (11 * 7) * 15 = 385 m^3 5. 5 cm area of base = 27 cm^2 V = 1/3 Bh pentagon (27) * 5 = 45 cm^3 6. 6 ft 4 ft 1 ft V = 1/3 Bh rectangle (4 * 1) * 6 = 8 ft^3 11.6 In Exercises 7-9, find the indicated measure. 7. A pyramid with a square base has a volume of 128 cubic inches and a height of 6 inches. Find the side length of the square base. V = 1/3 Bh 128 = 1/3 (s^2) 6 128 = 2s^2 64 = s^2 8 = side 8. A pyramid with a rectangular base has a volume of 6 cubic feet. The length of the rectangular base is 3 feet and the width of the base is 1.5 feet. Find the height of the pyramid. V = 1/3 Bh 6 = 1/3 (3 * 1.5) h 6 = 1.5h 4 feet = h 9. A pyramid with a triangular base has a volume of 18 cubic centimeters. The height of the pyramid is 9 centimeters and the height of the triangular base is 3 centimeters. Find the width of the base. V = 1/3 Bh triangle = 1/3 (1/2 b * h) h = 1/3 (1/2 w * 3) 9 18 = (1/2 w) 9 36/9 = w 4 cm = width 10. The pyramids are similar. Find the volume of pyramid B. Volumes follow K^3 K^3 = Volume 3^3 = 125 2^3 = x 27/8 = 125/x 27x = 125 * 8 27x = 1000 x = 1000/27 x = 200/9 in^3 Pyramid A 15 in. V = 125 in^3 Pyramid B 10 in. K = 15/10 = 3/2 Side ratio