January 23, HW 3 GeometricSolids Key. Fundamentals of Algebra. Geometric Solids. Homework #3. Key
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1 Fundamentals of Algebra Geometric Solids Homework #3 Key 1
2 Problem #1 6 2
3 Problem #1 I Need To 6 I need to find the container that holds the largest volume of water, choosing between two cylinders and two cones 3
4 Problem #1 I Know I know the radius of cylinder A is 5 cm, the height is 3cm, the diameter of cylinder B is 5 cm, the height is 6cm so the radius of cylinder B is 2.5 cm and I know the volume of a cylinder is v = πr 2 h I know the radius of cone C is 5 cm, the height is 10cm, the radius of cone D is 6 cm, the height is 6 cm cm and I know the volume of a cone is is v = (1/3)πr 2 h I also know the units for all containers is cm, and the volume will be in cm 3, I also know that some containers may be better than others for racing and without a top I might not choos the container with the largest volume. There are 1000cm 3 in one liter and 3.79 (4) liters per gallon. 4
5 Problem # I Need To I Did Compute the volume of each container Cyl A v = πr 2 h Cyl B v = πr 2 h Cone C v = (1/3)πr 2 h Cone D v = (1/3)πr 2 h Compute the number of trips needed to fill one gallon, without spilling using 3786 cm 3 per gallon, or about 1206π 5
6 6
7 Problem # I Need To Therefore my answer is 7
8 6 cm 8
9 9
10 Problem #2 10
11 Problem #2 I Need To Split a block of clay 3x3x7 into two equal pieces. Then create a sphere and a cone. The diameter of the sphere and the diameter of the cone should be the same. I need to know what the diameter of the sphere is that I can make with half the clay, and I need to find the height of the cone so that the diameter of the cone is equal to the diameter of the sphere. Or I need to find the diameter of the cone if the height of the cone is the same as the diameter of the sphere. 11
12 Problem # I Know The volume of the block of clay is the formula for the volume of a sphere is the volume of the sphere is the formula for the volume of a cone is 12
13 Problem # I Need To I Did Calculate the diameter of the sphere from the volume d = 4 in Use the diameter of the cone to Calculate the height of the cone from the volume 13
14 I Need To Therefore my answer is a) The height of the cone is 7.5 inches so the diameter of the cone can be equal to the diameter of the sphere, and they can have equal volume (each using half the clay) a) If the height of the cone is 4 inches so the height of the cone can be equal to the diameter of the sphere, and they can have equal volume (each using half the clay) then the diameter of the cone is 5.4 inches v = 1/3(3.14)(5.4/2)^2(4) = 30.5 in 3 14
15 15
16 Problem #3 16
17 4.5' in diameter = 2.25 ' radius cubic yards of concrete/piller pillars/truckload 17
18 Problem #4 18
19 19
20 Problem #5 20
21 21
22 22
23 Problem #7 10" 10" 5" 10" 10" 23
24 10" 10" 10" 5" 10" = (1/3)(π)(25)(10) 24
25 End 25
26 Problem #7 10" 10" 5" 10" 10" 26
27 Problem # I Need To 27
28 Problem # I Know = (1/3)(π)(25)(10) 28
29 Problem # I Know = (1/3)(π)(25)(10) 29
30 Problem # I Need To I Did = (1/3)(π)(25)(10) 30
31 Problem # I Need To Therefore my answer is = (1/3)(π)(25)(10) 31
32 32
33 Problem # I Need To 33
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Worksheets for GCSE Mathematics Volume and Surface Area mr-mathematics.com Maths Resources for Teachers Shape Volume & Surface Area Worksheets Contents Differentiated Independent Learning Worksheets Volume
Volume of Prisms & Cylinders
4.4.D1 Volume of Prisms & Cylinders Recall that the volume of a three-dimensional figure is the number of nonoverlapping cubic units contained in the interior of the figure. For example, the prism at right