Answer:
a) Lateral area of the solid = 2011.43 [tex]cm^{2}[/tex]
b) Surface area of the solid = 2544 [tex]cm^{2}[/tex]
Step-by-step explanation:
a) Lateral area of the figure = 2[tex]\pi[/tex]rh
where; r is the radius of the cylinder, and h is its height.
Lateral area of the figure = 2 x [tex]\frac{22}{7}[/tex] x 10 x 32
= 2011.43 [tex]cm^{2}[/tex]
b) The surface area = 2[tex]\pi[/tex]r(r + h) - 2([tex]\frac{1}{2}[/tex] x b x h)
= 2[tex]\pi[/tex]r(r + h) - (b x h)
The height of the isosceles triangle can be determined by applying the Pythagoras theorem to have,
[tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]h^{2}[/tex]
100 = 36 + [tex]h^{2}[/tex]
[tex]h^{2}[/tex] = 100 - 36
= 64
h = [tex]\sqrt{64}[/tex]
= 8
h = 8 cm
The surface area of the solid = 2 x [tex]\frac{22}{7}[/tex] x 10 (10 + 32) - 12 x 8
= 2640 - 96
= 2544
The surface area of the solid is 2544 [tex]cm^{2}[/tex].
