Name: 3-D Shapes Surface Area and Volume Notes
Brand: EduBirdie
Rating: 5.0 (41 reviews)

University:
South Plains College
Course:
MATH 1332 | Contemporary Mathematics
Academic year:

2024
Views:

404

Pages:

4
Author:

Alexia V.

Name MATH 1332 Notes 3.4 MATH 0332/1332 Notes 4.4 3-D Shapes, Surface Area and Volume Space Figures and Polyhedra Definition: Space figures are three-dimensional figures. These include figures such prisms, pyramids, cylinders, cones, and spheres. Examples of Space Figures Cone Prisms Pyramids Cylinders Sphere Definition: Polyhedraare space frgures that have faces that arc polygons. These include prisms and pyramids. Surface Area and Volume Deinition: The suriace area of a space figure is a measure ofthe total area occupied by the surface of the object. It would be the measure of the total area covered if the objectwere "peeled" and the peel was laid llat. Surface area is measured in square units. Definition: The volume of aspace figure is a measure of capacity (how much the object will hold). Volume is athree-dimensional measurement so it is mcasured in cubic units. Formulas for Some Common Space Figures Rectangular Prism Cube h SA = 2lw+ 2lh +2wh V= lwh SA= 6s V=s3 Cylinder Sphere SA = 2rr² + 2nrh, SA = 4? V=nr²h Pyramid Cone SA = A h faces SA= add up the areas of the vr? + h?+rr2 V=Bhwhere where.B is the area of the base polyhedralcylinder by finding the area of a of area surface always findthe MSurface Area Note: You can areas. those eachface and adding up B represents the area of where Bh V= by found anyprism/cylinder can be represents the area of the Volume Note: The volume ofpyramidlcone can befound by V =Bh where B any the base. The volume of base. Find the surface area and volume of thefollowing. 1. Rectangular Prism S= 22wt2h 2lw V= =44Pt S 3/6)(8) Luh: ]: 324iY 2. Sphere L01.86m (724) r--m S=27+2rh 3. Cylinder 342N 16 yd 28 yd d<25yd, r-14yds (9)U) 27/4)+2r 4. Find the volume of the square pyramid shown. 9m 108m 3 6m 6m B-s(O)=36 5. Find the volume (in cubic feet) of a construction cone, which has a height of 3 feet and a base radius of6 inches. E.76PS 6. If the surface area of a cube is 96 square centimeters, what is the volume of the cube? V=s, S =4cm 7. A bpx (rectangular prism) has atotal surface area of 94 square inches. If the length of the box is sinches and the width is 3/nches,what is the height of the box? he? S=2wt 2lht2n q4=245YIY2US+2(3)h q4 -30 +loh 8. If youdouble the radius of asphere, the surface area increases by a factor of_ volune increases by a factor of and the 9. Given the tank below in the shape of a rectangular prism. h=Y6|n a 6ft Find the volume of the rectangular prism in cubic inchs yx &32n (ab) V= dwh = 72036 gallon. If there are 231 cubic inches ner b You are going to fill this with a liquid that costs $4 this tank? up fill to you cost it will in a gallon, hoW much money 24 8, 83 RAY6O 14s3230878/ 23) 23] or the ceiling). On one wall., 10. You are going to paint the walls of the room shown (not the floor not need to be painted. there is a door that measures 7 feet by 3 feet and that door does 9ft DoyCneas 35 ft a. What is the square footage of the area you will need to paint? 4pt by ePt anl 2 meosng 9Pt b 3set 2wallSreusrng 2c4)0)hccss5 An q40p he pamz 990-l 964P b. One can of paint covers 400 square feet. How many cans of paint will you need to buy if you are going to put two coa~~cuns~~

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