Answer:
i. Curved surface area = 2310 [tex]cm^{2}[/tex]
ii. Total surface area = 3696 [tex]cm^{2}[/tex]
iii. volume = 12936 [tex]cm^{3}[/tex]
Step-by-step explanation:
Perimeter of the circular base = circumference of the circle = 132 cm
circumference of a circle = 2[tex]\pi[/tex]r
132 = 2[tex]\pi[/tex]r
r = [tex]\frac{132}{2\pi }[/tex]
= [tex]\frac{66}{\pi }[/tex]
r = 66 x [tex]\frac{7}{22}[/tex]
= 3 x 7
= 21
radius = 21 cm
vertical height, h = 28 cm
Thus applying the Pythagoras theorem,
[tex]l^{2}[/tex] = [tex]h^{2}[/tex] + [tex]r^{2}[/tex]
= [tex]28^{2}[/tex] + [tex]21^{2}[/tex]
= 784 + 441
= 1225
l = [tex]\sqrt{1225}[/tex]
l = 35 cm
The slant height is 35 cm.
i. Curved surface area = [tex]\pi[/tex]rl
= [tex]\frac{22}{7}[/tex] x 21 x 35
= 22 x 3 x 35
= 2310
curved surface area of the cone is 2310 [tex]cm^{2}[/tex].
ii. Total surface area = [tex]\pi r^{2}[/tex] + [tex]\pi[/tex]rl
= [tex]\pi[/tex]r(r + l)
= [tex]\frac{22}{7}[/tex] x 21 (21 + 35)
= 22 x 3 x 56
= 3696
The total surface area of the cone is 3696 [tex]cm^{2}[/tex].
iii. volume of a cone = [tex]\frac{1}{3}[/tex][tex]\pi r^{2}[/tex]h
= [tex]\frac{1}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex]21^{2}[/tex] x 28
= 12936
The volume of the cone is 12936 [tex]cm^{3}[/tex]
