Answer:
a) [tex]SA = 522.9~cm^2[/tex]
b) [tex] V_{cone} = 670.2~cm^3 [/tex]
c) [tex] V_{empty} = 1340.4~cm^3 [/tex]
Step-by-step explanation:
a)
For a cone,
[tex] SA = \pi r (L + r) [/tex]
where L = slant height
[tex] L = \sqrt{r^2 + h^2} [/tex]
We have r = 8 cm; h = 10 cm
[tex]L = \sqrt{(8~cm)^2 + (10~cm)^2}[/tex]
[tex]L = \sqrt{164~cm^2}[/tex]
[tex]SA = (\pi)(8~cm)(\sqrt{164~cm^2} + 8~cm)[/tex]
[tex]SA = 522.9~cm^2[/tex]
b)
[tex] V_{cone} = \dfrac{1}{3}\pi r^2 h [/tex]
[tex] V_{cone} = \dfrac{1}{3}(\pi)(8~cm)^2(10~cm) [/tex]
[tex] V_{cone} = 670.2~cm^3 [/tex]
c)
[tex] V_{cylinder} = \pi r^2 h [/tex]
empty space = volume of cylinder - volume of cone
[tex] V_{empty} = V_{cylinder} - V_{cone} [/tex]
[tex] V_{empty} = \pi r^2 h - \dfrac{1}{3}\pi r^2 h [/tex]
[tex] V_{empty} = (\pi)(8~cm)^2(10~cm) - \dfrac{1}{3}(\pi)(8~cm)^2(10~cm) [/tex]
[tex] V_{empty} = 1340.4~cm^3 [/tex]
