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Math Concepts in Three-Dimensional Figures Explained

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Learn about volume, area, perimeter, circumference, and surface area of various shapes including cubes, prisms, cylinders, pyramids, cones, spheres, and circles. Understand formulas through word problems.

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Math Concepts in Three-Dimensional Figures Explained

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  1. By Angelica Gonzalez 2nd Period 8th Grade Math Chart

  2. Volume • The amount of space, measured in cubic units, that an object takes up. • Prism: V=Bh • Cylinder: V=Bh • Pyramid: V=1/3Bh • Cone: V=1/3Bh • Sphere: V=4/3(3.14)r^3

  3. Word Problem • A cylinder has a diameter of 14 inches and a height of 21 inches. What is its volume? A=3.14(7^2) A=3.14(49) A=153.86 V=153.86(21) 14 in. 21 in. V = 3,231.06 in. V=Bh A=3.14(r^2)

  4. Pi • The ratio of the circumference to the diameter of a circle; equal to about 3.141592+.

  5. Word Problem

  6. Area • The area of a figure is the number of squares required to cover it completely. • Square: A=s^2 • Rectangle: A=lw or A=bh • Triangle: A=1/2bh or A=bh/2 • Circle: A=(3.14)r^2

  7. Word Problem • A circle has a radius of 5 cm. Find the area. A = 3.14 (r^2) A=3.14(5)^2 A=3.14(25) 5 cm. A = 78.5 cm.

  8. Perimeter • A path that surrounds an area. • Square: P=4s • Rectangle: P=2l+2w or P=2(l+w)

  9. Word Problem • What is the perimeter of this figure? P = 2(l + w) P = 2 (9 +4) P = 2 (13) P = 26 in. 4 in. 9 in.

  10. Circumference • The size of something as given by the distance around it. • Circle: C=2(3.14)r

  11. Word Problem • If a circle has a diameter of 8 inches, what is the circumference? 8 in. 3.14 * 8 = 25.12 in.

  12. Surface Area • A measure of the number of square units needed to cover the faces or surfaces of a figure. • Cube(total): S=6s^2 • Prism(lateral): S=Ph • Prism(total): S=Ph+2B • Pyramid(lateral): S=1/2Pl • Pyramid(total): S=1/2Pl+B • Cylinder(lateral): S=2(3.14)rh • Cylinder(total): S=2(3.14)rh+2(3.14)r^2 or S=2(3.14)r(h+r)

  13. Word Problem • Find the lateral surface area a cylinder with a height of 12 cm. and a diameter of 8 cm. 8 cm. S = 2(3.14)rh S = 6.28 (4) h S = 25.12 (12) 12 cm. S = 301.44 cm.

  14. Pythagorean Theorem • a^2+b^2=c^2

  15. Word Problem

  16. Simple Interest Formula • I = prt

  17. Word Problem

  18. P • P represents the perimeter of the base of a three-dimensional figure.

  19. Word Problem

  20. B • B represents the area f the base of a three-dimensional figure.

  21. Word Problem

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