Question

Please help me I really need help i beg of u due today

Answer 1

The volume of the observatory is 497.43
`feet^(3)`

Explanation:

i) The diameter of the floor is 10 feet. The floor is circular and has a radius,

r =
`(10)/(2)` = 5 feet.

Therefore the area of the circular floor of the observatory

=
`\pi r^(2)` = 3.14159 ×
`5^(2)` = 78.54
`feet^(2)`

ii) The observatory is made up of two parts

a) 3 foot tall cylinder

∴ volume of cylinder =
`\pi r^(2)` × h

= 78.54 × 3

= 235.62
`feet^(3)`

b) hemisphere =
`(1)/(2)` ×
`(4)/(3) \pi r^(3)` = 0.6667 × 78.54 × 5 = 261.81
`feet^(3)`

c) Therefore the total volume of the observatory is = a) + b)

= 235.62 + 261.81 = 497.43
`feet^(3)`