The answers of the given geometrical shapes are:
1. 226.29 cubic yard
2. 46.1 cubic inches
3. 2413.71 cubic inches
4. 234.67 cubic millimeter
5. 340.48 cubic yards
6. 113.14 cubic feet
7. 528 cubic centimeter
8. 905.14 cubic centimeter
9. 56.57 cubic feet
what is mensuration?
Mensuration is the branch of geometry that deals with measurement of volumes and areas of geometrical shapes.
Analysis:
1. volume of cylinder =π [tex]r^{2}[/tex]h. where r = 6/2 = 3 yard, h = 8 yard
= [tex]\frac{22}{7}[/tex] x [tex]3^{2}[/tex] x 8 = 226.29 cubic yard
2. volume of cone = [tex]\frac{1}{3}[/tex] x π [tex]r^{2}[/tex]h. where r = 2inches, h = 11
= [tex]\frac{1}{3}[/tex] x [tex]2^{2}[/tex] x [tex]\frac{22}{7}[/tex] x 11 = 46.1 cubic inches
3. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 8, h = 12
= [tex]\frac{22}{7}[/tex] x [tex]8^{2}[/tex] x 12 = 2413.71 cubic inches
4. volume of cone = [tex]\frac{1}{3}[/tex] x π [tex]r^{2}[/tex]h. where r = 4, h = 14
= [tex]\frac{1}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex]4^{2}[/tex] x 14 = 234.67 cubic millimeter
5. volume of cone = [tex]\frac{1}{3}[/tex] x π [tex]r^{2}[/tex]h. where r = 5, h = 13
= [tex]\frac{1}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex]5^{2}[/tex] x 13 = 340.48 cubic yards
6. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 3, h = 4
= [tex]\frac{22}{7}[/tex] x [tex]3^{2}[/tex] x 4 = 113.14 cubic feet
7. volume of cone = [tex]\frac{1}{3}[/tex] x π [tex]r^{2}[/tex]h. r = 6, h = 14
= [tex]\frac{1}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex]6^{2}[/tex] x 14 = 528 cubic centimeter
8. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 6, h = 8
= [tex]\frac{22}{7}[/tex] x [tex]6^{2}[/tex] x 8 = 905.14 cubic centimeter
9. volume of cylinder = π [tex]r^{2}[/tex]h. where r = 1.5, h = 4
= [tex]\frac{22}{7}[/tex] x [tex]1.5^{2}[/tex] x 4 = 56.57 cubic feet
In conclusion, the volume of cylinders and cones for the given dimensions are:
1. 226.29 cubic yard
2. 46.1 cubic inches
3. 2413.71 cubic inches
4. 234.67 cubic millimeter
5. 340.48 cubic yards
6. 113.14 cubic feet
7. 528 cubic centimeter
8. 905.14 cubic centimeter
9. 56.57 cubic feet
Learn more about mensuration: brainly.com/question/18541562
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