Question

Please solve with explanation I’ve been asking all day (this is not a multiple choice question)

Answer 1

a)
`SA = 522.9~cm^2`

b)
`V_(cone) = 670.2~cm^3`

c)
`V_(empty) = 1340.4~cm^3`

Explanation:

a)

For a cone,

`SA = \pi r (L + r)`

where L = slant height

`L = √(r^2 + h^2)`

We have r = 8 cm; h = 10 cm

`L = √((8~cm)^2 + (10~cm)^2)`

`L = √(164~cm^2)`

`SA = (\pi)(8~cm)(√(164~cm^2) + 8~cm)`

`SA = 522.9~cm^2`

b)

`V_(cone) = (1)/(3)\pi r^2 h`

`V_(cone) = (1)/(3)(\pi)(8~cm)^2(10~cm)`

`V_(cone) = 670.2~cm^3`

c)

`V_(cylinder) = \pi r^2 h`

empty space = volume of cylinder - volume of cone

`V_(empty) = V_(cylinder) - V_(cone)`

`V_(empty) = \pi r^2 h - (1)/(3)\pi r^2 h`

`V_(empty) = (\pi)(8~cm)^2(10~cm) - (1)/(3)(\pi)(8~cm)^2(10~cm)`

`V_(empty) = 1340.4~cm^3`