Answer:
1. The volume of the cylinder is 263 [tex]cm^{3}[/tex].
2. The volume of the cylinder is 12 [tex]m^{3}[/tex].
3. The volume of the cylinder is 3165.1 [tex]cm^{3}[/tex].
4. The radius of the cylinder is 3.6 cm.
5a. Area of the base is 50.2 [tex]cm^{2}[/tex].
5b. The curved surface area of the pencil holder is 351.7 [tex]cm^{2}[/tex].
5c. The surface are of the pencil holder is 452.2 [tex]cm^{2}[/tex].
Step-by-step explanation:
1. The given shape is a cylinder, so that;
volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
= 3.14 x [tex](3.8)^{2}[/tex] x 5.8
= 262.98128
The volume of the cylinder is 263 [tex]cm^{3}[/tex].
2. This is also a cylinder, but with a given diameter.
radius = [tex]\frac{diameter}{2}[/tex]
= [tex]\frac{1.2}{2}[/tex] = 0.6 m
volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
= 3.14 x [tex](0.6)^{2}[/tex] x 10.6
= 11.98224
The volume of the cylinder is 12 [tex]m^{3}[/tex].
3. volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
= 3.14 x [tex]6^{2}[/tex] x 28
= 3165.12
The volume of the cylinder is 3165.1 [tex]cm^{3}[/tex].
4. volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
239 = 3.14 x [tex]r^{2}[/tex] x 6
239 = 18.84 [tex]r^{2}[/tex]
[tex]r^{2}[/tex] = [tex]\frac{239}{18.84}[/tex]
= 12.6858
r = [tex]\sqrt{12.6858}[/tex]
= 3.5617
The radius of the cylinder is 3.6 cm.
5. Area of the base = [tex]\pi[/tex][tex]r^{2}[/tex]
radius = [tex]\frac{diameter}{2}[/tex]
= [tex]\frac{8}{2}[/tex] = 4 cm
Area of the base = 3.14 x [tex]4^{2}[/tex]
= 50.24
Area of the base is 50.2 [tex]cm^{2}[/tex].
5b. Area of the curved surface of the pencil holder = 2[tex]\pi[/tex]rh
= 2 x 3.14 x 4 x 14
= 351.68
The curved surface area of the pencil holder is 351.7 [tex]cm^{2}[/tex].
5c. Surface area of the pencil holder = 2[tex]\pi[/tex]rh + 2[tex]\pi[/tex][tex]r^{2}[/tex]
= 2[tex]\pi[/tex]r(h + r)
= 2 x 3.14 x 4 (14 + 4)
= 452.16
The surface are of the pencil holder is 452.2 [tex]cm^{2}[/tex].
